linear equations
DESCRIPTION
Students learn to define and identify linear equations. They also learn the definition of Standard Form of a linear equation.Students also learn to graph linear equations using x and y intercepts.TRANSCRIPT
Linear Equations Linear Equations
Identify linear equations and functions.
Write linear equations in standard form and graph them.
1) linear equation2) linear function3) standard form4) y-intercept5) x-intercept
Sara has 4 hours after dinner to study and dohomework. She has brought home algebra 2and chemistry.
Linear Equations Linear Equations
y
x
6
0
4-2-2
2
6
-2 6
0
-2
6
2
4
4 yx
Sara has 4 hours after dinner to study and dohomework. She has brought home algebra 2and chemistry.
If she spends x hours on algebra and y hours on chemistry, a portion of the graphof the equation x + y = 4 can be used to relate how much time she spends on each.
Linear Equations Linear Equations
y
x
6
0
4-2-2
2
6
-2 6
0
-2
6
2
4
4 yx
Sara has 4 hours after dinner to study and dohomework. She has brought home algebra 2and chemistry.
If she spends x hours on algebra and y hours on chemistry, a portion of the graphof the equation x + y = 4 can be used to relate how much time she spends on each.
An equation such as x + y = 4 is called a linear equation.
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
The variables may not be multiplied together or appear in a ____________.
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
The variables may not be multiplied together or appear in a ____________.denominator
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
The variables may not be multiplied together or appear in a ____________.
A linear equation does not contain variables with exponents other than __.
denominator
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
The variables may not be multiplied together or appear in a ____________.
A linear equation does not contain variables with exponents other than __.1
denominator
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
The variables may not be multiplied together or appear in a ____________.
A linear equation does not contain variables with exponents other than __.1
denominator
The graph of a linear equation is always a ____.
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
The variables may not be multiplied together or appear in a ____________.
A linear equation does not contain variables with exponents other than __.1
denominator
The graph of a linear equation is always a ____.line
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
The variables may not be multiplied together or appear in a ____________.
A linear equation does not contain variables with exponents other than __.1
denominator
The graph of a linear equation is always a ____.line
Linear Equations
735 yx
9x
1536 ts
xy21
Linear Equations Linear Equations
A linear equation has no operations other than:
________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant
The variables may not be multiplied together or appear in a ____________.
A linear equation does not contain variables with exponents other than __.1
denominator
The graph of a linear equation is always a ____.line
Linear Equations Not Linear Equations
735 yx
9x
1536 ts
xy21
847 2 ba
5 xy
1 xyx
xy
1
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy No!
Linear Equations Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy No!
Two variables are multiplied together.
Linear Equations Linear Equations
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
Linear Equations Linear Equations
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
The linear function P(d) = 62.5d + 217can be used to find the pressure (lb/ft2)at a depth of d ft. below the surface ofthe water.
Linear Equations Linear Equations
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
The linear function P(d) = 62.5d + 217can be used to find the pressure (lb/ft2)at a depth of d ft. below the surface ofthe water.
Find the pressure at a depth of 350 feet.
Linear Equations Linear Equations
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
The linear function P(d) = 62.5d + 217can be used to find the pressure (lb/ft2)at a depth of d ft. below the surface ofthe water.
Find the pressure at a depth of 350 feet.
P(d) = 62.5d + 217
Linear Equations Linear Equations
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
The linear function P(d) = 62.5d + 217can be used to find the pressure (lb/ft2)at a depth of d ft. below the surface ofthe water.
Find the pressure at a depth of 350 feet.
P(d) = 62.5d + 217
P(350) = 62.5(350) + 217
Linear Equations Linear Equations
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
The linear function P(d) = 62.5d + 217can be used to find the pressure (lb/ft2)at a depth of d ft. below the surface ofthe water.
Find the pressure at a depth of 350 feet.
P(d) = 62.5d + 217
P(350) = 62.5(350) + 217
P(350) = 22,092
Linear Equations Linear Equations
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
To avoid decompressionsickness, it is recommendedthat divers ascend no fasterthan 30 feet per minute.
The linear function P(d) = 62.5d + 217can be used to find the pressure (lb/ft2)at a depth of d ft. below the surface ofthe water.
Find the pressure at a depth of 350 feet.
P(d) = 62.5d + 217
P(350) = 62.5(350) + 217
P(350) = 22,092
The pressure at a depth of 350 feet is about 2 000,22ftlb
Linear Equations Linear Equations
Any linear function can be written in standard form.
Linear Equations Linear Equations
Any linear function can be written in standard form.
Standard Form of a Linear Function
Linear Equations Linear Equations
Any linear function can be written in standard form.
Standard Form of a Linear Function
The standard form of a linear function is Ax + By = C, where A > 0,
Linear Equations Linear Equations
Any linear function can be written in standard form.
Standard Form of a Linear Function
The standard form of a linear function is Ax + By = C, where A > 0,
A and B are not both zero.
Linear Equations Linear Equations
Any linear function can be written in standard form.
Standard Form of a Linear Function
The standard form of a linear function is Ax + By = C, where A > 0,
A and B are not both zero.
Also, A, B, and C are integers whose greatest common factor is 1
Linear Equations Linear Equations
Standard Form of a Linear Function
The standard form of a linear function is Ax + By = C, where A > 0,
A and B are not both zero.
Also, A, B, and C are integers whose greatest common factor is 1
Linear Equations Linear Equations
Write the equation in Standard Form:
43 xy
Standard Form of a Linear Function
The standard form of a linear function is Ax + By = C, where A > 0,
A and B are not both zero.
Also, A, B, and C are integers whose greatest common factor is 1
Linear Equations Linear Equations
Write the equation in Standard Form:
43 xy
43 yx
Standard Form of a Linear Function
The standard form of a linear function is Ax + By = C, where A > 0,
A and B are not both zero.
Also, A, B, and C are integers whose greatest common factor is 1
Linear Equations Linear Equations
Write the equation in Standard Form:
62
1
2
1 yx
Standard Form of a Linear Function
The standard form of a linear function is Ax + By = C, where A > 0,
A and B are not both zero.
Also, A, B, and C are integers whose greatest common factor is 1
Linear Equations Linear Equations
Write the equation in Standard Form:
62
1
2
1 yx
12 yx
In the previous lesson, you graphed functions by using a table of values.
Linear Equations Linear Equations
In the previous lesson, you graphed functions by using a table of values.
Since two points determine a line, there are quicker ways to graph linear functions.
Linear Equations Linear Equations
In the previous lesson, you graphed functions by using a table of values.
Since two points determine a line, there are quicker ways to graph linear functions.
One way is to find the points at which the graph intersects each axis and then connectthem with a line.
y
x
Linear Equations Linear Equations
In the previous lesson, you graphed functions by using a table of values.
Since two points determine a line, there are quicker ways to graph linear functions.
One way is to find the points at which the graph intersects each axis and then connectthem with a line.
y
x
The y-coordinate of the point at which the graphcrosses the y-axis is called the ____________.
Linear Equations Linear Equations
(0, 3)
In the previous lesson, you graphed functions by using a table of values.
Since two points determine a line, there are quicker ways to graph linear functions.
One way is to find the points at which the graph intersects each axis and then connectthem with a line.
y
x
The y-coordinate of the point at which the graphcrosses the y-axis is called the ____________.y - intercept
(0, 3)
Linear Equations Linear Equations
In the previous lesson, you graphed functions by using a table of values.
Since two points determine a line, there are quicker ways to graph linear functions.
One way is to find the points at which the graph intersects each axis and then connectthem with a line.
y
x
The y-coordinate of the point at which the graphcrosses the y-axis is called the ____________.y - intercept
The x-coordinate of the point at which the graphcrosses the x-axis is called the ____________.
(0, 3)
(-4, 0)
Linear Equations Linear Equations
In the previous lesson, you graphed functions by using a table of values.
Since two points determine a line, there are quicker ways to graph linear functions.
One way is to find the points at which the graph intersects each axis and then connectthem with a line.
y
x
The y-coordinate of the point at which the graphcrosses the y-axis is called the ____________.y - intercept
The x-coordinate of the point at which the graphcrosses the x-axis is called the ____________.x - intercept
(0, 3)
(-4, 0)
Linear Equations Linear Equations
In the previous lesson, you graphed functions by using a table of values.
Since two points determine a line, there are quicker ways to graph linear functions.
One way is to find the points at which the graph intersects each axis and then connectthem with a line.
y
x
The y-coordinate of the point at which the graphcrosses the y-axis is called the ____________.y - intercept
The x-coordinate of the point at which the graphcrosses the x-axis is called the ____________.x - intercept
(0, 3)
(-4, 0)
Linear Equations Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
Linear Equations Linear Equations
1535 yx
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
Linear Equations Linear Equations
1535 yx
15)0(35 x
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.(0, 5)
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
5y
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.(0, 5)
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
5y
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
5y
(0, 5)
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.(0, 5)
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
5y
Linear Equations Linear Equations
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Using Glencoe’s Algebra 2 text,© 2005
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