Warm Warm UpUp

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Graph the linear functions.

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INTERCEPTS OF GRAPHSINTERCEPTS OF GRAPHS

ObjectivesObjectives

Graph and interpret linear Functions. (AF 3.0)Graph and interpret linear Functions. (AF 3.0)

Represent quantitative relationships Represent quantitative relationships graphically and interpret the meaning of a graphically and interpret the meaning of a specific part of the graph in the situation specific part of the graph in the situation represented by the graph. (AF 1.5) represented by the graph. (AF 1.5)

INTERCEPTS OF A INTERCEPTS OF A GRAPHGRAPH

InterceptsIntercepts- - points at which the graph intersects points at which the graph intersects the the xx-- or or yy--axis.axis.

What number do the x- and y- intercepts What number do the x- and y- intercepts have in common?have in common?

Finding intercepts:Finding intercepts: An An xx-intercept is written as the ordered pair (-intercept is written as the ordered pair (xx, ,

0).0). A A yy-intercept is written as the ordered pair (0, -intercept is written as the ordered pair (0, yy).).

The graph of any The graph of any linear linear equation in two variables equation in two variables is a is a straight linestraight line..

y

x

Intercepts

• Finding intercepts can be helpful when graphing.

• The x-intercept is the point where the line crosses the x-axis.

• The y-intercept is the point where the line crosses the y-axis.

x - intercept

y - intercept

Finding the Finding the interceptsintercepts

1)1) To find the x - interceptTo find the x - intercept of a line, substitute of a line, substitute y = 0 into the equation and solve for x.y = 0 into the equation and solve for x.

2) To find the y - intercept2) To find the y - intercept of a line, substitute of a line, substitute x = 0 into the equation and solve for y.x = 0 into the equation and solve for y.

Finding the x - interceptFinding the x - intercept Find the x-intercept of the graph of the equation y =2x-6Find the x-intercept of the graph of the equation y =2x-6

To find the x-intercept: To find the x-intercept:

substitute in ZERO for y and solve for y.substitute in ZERO for y and solve for y.

y = 2x-6 write the equationy = 2x-6 write the equation

0=2x -6 substitute 0 for y 0=2x -6 substitute 0 for y

+6 +6 +6 +6 solve for xsolve for x

6=2x6=2x

3=x 3=x

Thus, the x-intercept is (3,0).Thus, the x-intercept is (3,0).

Finding the y - interceptFinding the y - intercept

Find the y-intercept of the graph of the equation y =2x-6Find the y-intercept of the graph of the equation y =2x-6

To find the y-intercept: To find the y-intercept:

substitute in ZERO for x and solve for y.substitute in ZERO for x and solve for y.

y = 2x-6 write the equationy = 2x-6 write the equation

y = 2(y = 2(00) -6 substitute 0 for x ) -6 substitute 0 for x

y = 0-6y = 0-6 solve for ysolve for y

y = -6y = -6

Thus, the y- intercept is (0,-6).Thus, the y- intercept is (0,-6).

Find the intercepts of y = Find the intercepts of y = 4x+44x+4

To find the x - intercept: To find the x - intercept:

Let y = 0 Let y = 0

y = 4x+4y = 4x+4

0=4x +40=4x +4

-4 -4 -4 -4

solve for xsolve for x -4=4x-4=4x

-1 = x -1 = x Thus, the x-intercept is Thus, the x-intercept is

(-1,0).(-1,0).

To find the y - To find the y - intercept: intercept:

let x=0let x=0 y = 4x+4 y = 4x+4

y = y = 4(4(00) +4) +4 y = 0+4y = 0+4

solve for ysolve for y y = 4y = 4

Thus, the y -intercept Thus, the y -intercept is (0,4). is (0,4).

You tryYou try Find the intercepts of the graph of y = -Find the intercepts of the graph of y = -

3x+63x+6 To find the x - intercept: To find the x - intercept:

Let y = 0 Let y = 0

y = -3x+6y = -3x+6

0=-3x +60=-3x +6

-6 -6 -6 -6

solve for xsolve for x -6=-3x-6=-3x

2= x 2= x Thus, the x-intercept is Thus, the x-intercept is

(2,0).(2,0).

To find the y - To find the y - intercept: intercept:

let x=0let x=0 y = -3x+6 y = -3x+6

y y = -3(= -3(00) +6) +6 y = 0+6y = 0+6

solve for ysolve for y y = 6y = 6

Thus, the y -intercept Thus, the y -intercept is (0,6). is (0,6).

Identify the Identify the interceptsintercepts

1) x - intercept:1) x - intercept:

y - intercept:y - intercept:

2) x - intercept:2) x - intercept:

y - intercept:y - intercept:

3) x - intercept:3) x - intercept:

y - intercept:y - intercept:4

2

2

-1

-2

-2

Sketch a graph using the Sketch a graph using the interceptsintercepts

x - intercept: 4 x - intercept: 4

y - intercept: 3

Sketch a graph using the Sketch a graph using the interceptsintercepts

1) x - intercept: -21) x - intercept: -2

y - intercept: 3y - intercept: 3

2) x - intercept: 22) x - intercept: 2

y - intercept: 4y - intercept: 4

3) x - intercept:-33) x - intercept:-3

y - intercept:-4y - intercept:-4