ObjectiveThe student will be able to:

1. Find the x- and y-intercepts of linear equations.

2. Use the intercepts to make a “quick graph” of the linear function.

NCSCOS: 1.02 & 3.03Designed by Skip Tyler, Varina High School, edited by Leigh Harris, South Lenoir High School

What does it mean to INTERCEPT a pass in football?

The path of the defender crosses the path of the thrown football.

In algebra, what are x- and y-intercepts?

What are the x- and y-intercepts?The x-intercept is where

the graph crosses the x-axis. The y-coordinate is always 0.

The y-intercept is where the graph crosses the y-axis. The x-coordinate is always 0.

(2, 0)

(0, -6)

Find the x- and y-intercepts.1. x - 2y = 12

x-intercept: Plug in 0 for y.

x - 2(0) = 12

x = 12; (12, 0)

y-intercept: Plug in 0 for x.

0 - 2y = 12

y = -6; (0, -6)

x-intercept: Plug in 0 for y.

-3x - 5(0) = 9

-3x = 9

x = -3; (-3, 0)

y-intercept: Plug in 0 for x.

-3(0) + 5y = 9

5y = 9

y = ; (0, )9

5

9

5

Find the x- and y-intercepts.2. -3x + 5y = 9

x-intercept: Plug in 0 for y.

Does 0 = 7?

No! There is no x-intercept. None

What type of lines have no x-intercept?

Horizontal!

Remember VUXHOY!Remember VUXHOY! (what’s that, you say? just wait. . .I’ll tell you in a minute. . .)(what’s that, you say? just wait. . .I’ll tell you in a minute. . .)

Horizontal lines…y = 7…y-int = (0, 7)

Find the x- and y-intercepts.3. y = 7 ***Special case***

y-intercept: Plug in 0 for x.

Does 0 = 9?

No! There is no y-intercept. None

What type of lines have no y-intercept?

Vertical!

Remember VUXHOY!Remember VUXHOY!(hmmmmmm. . .there’s that word again. . . .patience. . .!)

Vertical lines…x = 9…x-int = (9, 0)

Find the x- and y-intercepts.4. x = 9 ***Special case***

Remember the word “VUXHOY”“VUXHOY”

(this will really be helpful later!!!)(this will really be helpful later!!!)

Vertical linesUndefined slope (no slope)X = number; This is the equation of the line.

Horizontal linesO - zero is the slopeY = number; This is the equation of the line.

What is the x-intercept of3x – 4y = 24?

1. (3, 0)

2. (8, 0)

3. (0, -4)

4. (0, -6)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

What is the y-intercept of-x + 2y = 8?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. (-1, 0)

2. (-8, 0)

3. (0, 2)

4. (0, 4)

What is the y-intercept ofx = 3?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. (3, 0)

2. (-3, 0)

3. (0, 3)

4. None

What is the x-intercept ofy = 3?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. (3, 0)

2. (-3, 0)

3. (0, 3)

4. None

Find the x- and y-intercepts of 2x + 3y = 6

using the TI-84 graphing calculator.Before using the calculator, you MUST

solve the equation for y first.

3y = -2x + 6

y = + 2

Type the equation in the “y =“ menu and graph it.

2

3

x

Your graph should look like this. It may vary depending on your window size.

The x-intercept is (3, 0)

Press 2ND, TABLE and scroll to find where the y-value is zero to find the x-intercept.

Now find the y-intercept!

Press 2ND TABLE (or you may still be there) to find the y-intercept.

y-intercept = (0, 2)