tlw identify linear equations and intercepts

Linear Functions

TLW identify linear equations and intercepts.

A linear equation is the equation of a line.The standard form of a linear equation is

Ax + By = C* A has to be positive and cannot be a

fraction.

Examples of linear equations

2x + 4y =8

6y = 3 – x

x = 1

-2a + b = 5

4

73

x y

Equation is in Ax + By =C form

Rewrite with both variables on left side … x + 6y =3

B =0 … x + 0 y =1

Multiply both sides of the equation by -1 … 2a – b = -5

Multiply both sides of the equation by 3 … 4x –y =-21

Examples of Nonlinear Equations

4x2 + y = 5 xy + x = 5s/r + r = 3

The exponent is 2

There is a radical in the equation

Variables are multiplied

Variables are divided

4x

The following equations are NOT in the standard form of Ax + By =C:

Determine whether the equation is a linear equation, if so write it in standard form.y = 5 – 2x

y = 5 – 2x Rewrite the equation

+ 2x+ 2x Add 2x to each side

2x + y = 5 Simplify

A = 2, B= 1, C=5 This IS a linear equation.

2xy -5y = 6

Determine whether the equation is a linear equation, if so write it in standard form.

Since the term 2xy has two variables, the equation cannot be written in the form Ax + By =0. Therefore, this is NOT a linear equation.


32 xy

Since the term x is raised to the second power, the equation cannot be written in the form Ax + By =0. Therefore, this is NOT a linear equation.

y = 6 – 3x


Rewrite the equation

y = 6 – 3x Add 3x to each side+ 3x+ 3x

Simplify3x +y = 6

A = 3, B= 1, C=6This IS a linear equation.


3541

yx

Multiply everything by the denominator to get rid of the fraction

)3541( yx(4)

x + 20y = 12

A = 1, B= 20, C=12This IS a linear equation.

-4x+7=2


X and Y interceptsThe x coordinate of the point at which the graph of an

equation crosses the x –axis is the x- intercept .The y coordinate of the point at which the graph of an

equation crosses the y-axis is called the y- intercept.

X- intercept (-x,0)

y- intercept (0, y)

3x + 2y = 9

Graph the linear equation using the x- intercept and the y intercept

To find the x- intercept, let y = 03x + 2y = 9 Original Equation

3x + 2(0) = 9 Replace y with 03x = 9 Divide each side by 3

x = 3

To find the y- intercept, let x = 03x + 2y = 9 Original Equation

Replace x with 0

Divide each side by 2

3(0) + 2y = 9

2y = 9 y = 4.5

Plot the two points and connect them to draw the line.

2x + y = 4

Graph the linear equation using the x- intercept and the y intercept

To find the x- intercept, let y = 0Original Equation

Replace y with 0

2x + y = 42x + (0) = 4

2x =4 Divide each side by 3

x = 2To find the y- intercept, let x = 0

2x + y = 42(0) + y = 4

y = 4

Original Equation

Replace x with 0

Simplify

Plot the two points and connect them to draw the line.

Identify the x- and y- intercepts given a table

X Y

-1 -6

0 -4

1 -2

2 0

3 2

X Y

-4 1

-3 0

-2 -1

-1 -2

0 -3

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 - 50 = 4y - 55 = 4y

= y

● (0, ) is the y-intercept

54

54

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) - 1g(x) = 0 - 1g(x) = -1

● (0, -1) is the y-intercept

*g(x) is the same as y

13

13

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

Graph by making a tableGraph 3

21

xy

Select values from the domain and make a table. Then graph the order pairs. Draw a line through the points

x y (x, y)-2 3)2(

21

-4 (-2, -4)0 3)0(

21

-3 (0, -3)

2 3)2(21

-2 (2, -2)

321

x

Graph by making a tableGraph

x y (x, y)

Select values from the domain and make a table. Then graph the order pairs. Draw a line through the points

2 xy

2 xy

Questions??

tlw identify linear equations and intercepts

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