graphing linear functions 1. graph linear functions. 2. write equations in standard form
TRANSCRIPT
Practice1) Solve for y: 2x + y = 4
2) Solve for y: 4x + 2y = -63) Solve for y: x – 3y = 6
Solve for y means isolate y. Get y all by itself!
1) Review: Solve for y 2x + y = 4
• Draw “the river”
• Subtract 2x from both sides
- 2x - 2x
y = -2x + 4
2) Solve for y: 4x + 2y = -6• Subtract 4x• Simplify• Divide both sides by 2• Simplify
- 4x - 4x
2y = -4x - 6
2 2
y = -2x - 3
3) Solve for y: x - 3y = 6
• Subtract x• Simplify• Divide both sides by -3• Simplify
- x - x
-3y = -x + 6
-3 -3
6
3
xy
2
3
xy
or
Graphing Steps
1) Isolate the variable (solve for y).
2) Make a t-table. If the domain is not given, pick your own values.
3) Plot the points on a graph.
4) Connect the points.
Make a t-tableIf f(x) = 2x + 4, complete a table using
the domain {-2, -1, 0, 1, 2}.
2(-2) + 4 = 0 (-2, 0)
2(-1) + 4 = 2 (-1, 2)
2(0) + 4 = 4 (0, 4)
2(1) + 4 = 6 (1, 6)
2(2) + 4 = 8 (2, 8)
x f(x)-2
-1
0
1
2
ordered pair
1) Given the domain {-2, -1, 0, 1, 2},
graph 3x + y = 6
-3(-2) + 6 = 12 (-2, 12)
-3(-1) + 6 = 9 (-1, 9)
-3(0) + 6 = 6 (0, 6)
-3(1) + 6 = 3 (1, 3)
-3(2) + 6 = 0 (2, 0)
x -3x + 6 ordered pair
1. Solve for y: 3x + y = 6
Subtract 3x - 3x - 3x
y = -3x + 62. Make a table
-2
-1
0
1
2
Bonus questions!What is the x-intercept?
(2, 0)What is the y-intercept?
(0, 6)Does the line increase or decrease?
Decrease
1) Given the domain {-2, -1, 0, 1, 2},
graph 3x + y = 63. Plot the points
(-2,12), (-1,9), (0,6), (1,3), (2,0)
4. Connect the points.
Standard FormAx + By = C
A, B, and C have to be integers
An equation is LINEAR (the graph is a straight line) if it can be written in standard form.
Determine whether each equation is a linear equation.
3) 4x = 7 + 2y
Can you write this in the form
Ax + By = C?
4x - 2y = 7
A = 4, B = -2, C = 7
This is linear!
4) 2x2 - y = 7Can you write it in standard form?
NO - it has an exponent!Not linear
5) x = 12x + 0y = 12
A = 1, B = 0, C = 12Linear
Determine whether each equation is a linear equation.
Here’s the cheat sheet! An equation that is linear does NOT contain the following:
1. Variables in the denominator
2. Variables with exponents
3. Variables multiplied with other variables.
xy = 12
32y
x
2 3y x
x and y -intercepts
●The x-intercept is the point where a line crosses the x-axis.The general form of the x-intercept is (x, 0).
The y-coordinate will always be zero.
●The y-intercept is the point where a line crosses the y-axis.The general form of the y-intercept is (0, y).
The x-coordinate will always be zero.
To find intercepts….
●To find the x-intercept, plug in 0 for y.
●To find the y-intercept, plug in 0 for x.
Find the x and y- interceptsof x = 4y – 5
● x-intercept:
● Plug in y = 0
x = 4y - 5
x = 4(0) - 5
x = 0 - 5
x = -5
● (-5, 0) is the
x-intercept
● y-intercept:
● Plug in x = 0
x = 4y - 5
0 = 4y - 5
5 = 4y
= y
● (0, ) is the
y-intercept
5
4
5
4
Find the x and y-interceptsof g(x) = -3x – 1*
●x-intercept
●Plug in y = 0
g(x) = -3x - 1
0 = -3x - 1
1 = -3x
= x
●( , 0) is the
x-intercept
●y-intercept
●Plug in x = 0
g(x) = -3(0) - 1
g(x) = 0 - 1
g(x) = -1
●(0, -1) is the
y-intercept
*g(x) is the same as y
1
3
1
3
Find the x and y-intercepts of 6x - 3y =-18
●x-intercept
●Plug in y = 0
6x - 3y = -18
6x -3(0) = -18
6x - 0 = -18
6x = -18
x = -3
●(-3, 0) is the
x-intercept
●y-intercept
●Plug in x = 0
6x -3y = -18
6(0) -3y = -18
0 - 3y = -18
-3y = -18
y = 6
●(0, 6) is the
y-intercept
Find the x and y-intercepts of x = 3
● y-intercept
● A vertical line never crosses the y-axis.
● There is no y-intercept.
● x-intercept
● Plug in y = 0.
There is no y. Why?
● x = 3 is a vertical line so x always equals 3.
● (3, 0) is the x-intercept.x
y
Find the x and y-intercepts of y = -2
● x-intercept
● Plug in y = 0.
y cannot = 0 because
y = -2.● y = -2 is a horizontal
line so it never crosses
the x-axis.
●There is no x-intercept.
● y-intercept
● y = -2 is a horizontal line
so y always equals -2.
● (0,-2) is the y-intercept.
x
y
Graphing Equations
●Example: Graph the equation -5x + y = 2Solve for y first.
-5x + y = 2 Add 5x to both sides y = 5x + 2
●The equation y = 5x + 2 is in slope-intercept form, y = mx+b. The y-intercept is 2 and the slope is 5. Graph the line on the coordinate plane.
Graph 4x - 3y = 12
●Solve for y first
4x - 3y =12 Subtract 4x from both sides
-3y = -4x + 12 Divide by -3
y = x + Simplify
y = x – 4
●The equation y = x - 4 is in slope-intercept form, y=mx+b. The y -intercept is -4 and the slope is . Graph the line on the coordinate plane.
Graphing Equations
12-3
43
43
43
-4-3