CONFIDENTIAL 1

Algebra1Algebra1

Using InterceptsUsing Intercepts

CONFIDENTIAL 2

Warm UpWarm Up

Solve each inequality and graph the solutions.

1) 3c > 12

2) -4 ≥ t 23) m ≥ -3 2

4) -2w > 14

CONFIDENTIAL 3

Using InterceptsA diver explored the ocean floor 120 feet below the surface

and then ascended at a rate of 30 feet per minute. The graph shows the diver’s elevation below sea level during the ascent.

0 1 2 3 4 5

-45-60

-15-30

Elev

atio

n (f

t)

time (min)

-105-120

-75-90

-135

The x-intercept is 4. It represents the time

that the diver reaches the surface or when

depth = 0.

The y-intercept is -120. It represents the

diver’s elevation at the start of the ascent

when time = 0.

CONFIDENTIAL 4

The y-intercept is the y-coordinate of thepoint where the graph intersects the y-axis.The x-coordinate of this point is always 0.

The x-intercept is the x-coordinate of the point where the graph intersects the x-axis. The y-

coordinate of this point is always 0.

CONFIDENTIAL 5

Finding Intercepts

0 2-2-4

2

-2-4

The graph intersects the y-axis at (0, -3).

Find the x- and y-intercepts.

A)

The y-intercept is -3.

The graph intersects the x-axis at (-4, 0).The x-intercept is -4.

Next page

CONFIDENTIAL 6

The x-intercept is 4.

B) 3x - 2y = 12

To find the x-intercept, replace y with 0 and solve for x.

3x - 2y = 123x - 2 (0) = 12

3x - 0 = 12

3x = 123x = 12 3 3

x = 4

The y-intercept is -6.

To find the y-intercept, replace x with 0 and solve for y.

3x - 2y = 123 (0) - 2y = 12

0 - 2y = 12

-2y = 12-2y = 12 -2 -2

y = -6

CONFIDENTIAL 7

Find the x- and y-intercepts.

Now you try!

0 2 44

246

8

x2

1)

2) -3x + 5y = 30

CONFIDENTIAL 8

Travel ApplicationThe Sandia Peak Tramway in Albuquerque, New Mexico, travels a distance of about 4500 meters to the top of Sandia Peak. Its

speed is 300 meters per minute. The function f (x) = 4500 - 300x gives the tram’s distance in meters from the top of the peak after x minutes. Graph this function and find the intercepts. What does each intercept

represent?

Neither time nor distance can be negative, so choose several nonnegative values for x. Use the function to

generate ordered pairs.

x 0 2 5 10 15f(x) = 4500 - 300x 4500 3900 3000 1500 0

Next page

CONFIDENTIAL 9

Graph the ordered pairs. Connect the points with a line.

• y-intercept: 4500. This is the starting distance from the top (time = 0).

• x-intercept: 15. This the time when the tram reaches the peak (distance = 0).

Remember, to graph a linear function, you need to plot only two ordered pairs. It is often simplest to find the

ordered pairs that contain the intercepts.

CONFIDENTIAL 10

Find the x- and y-intercepts.

Now you try!

1.) The school store sells pens for $2.00 and notebooks for $3.00. The equation 2x + 3y = 60 describes the number of pens x and notebooks y that you can buy for $60. Graph the function and find its intercepts.

CONFIDENTIAL 11

Use intercepts to graph the line described by each equation.Graphing Linear Equations by Using Intercepts

A) 2x - 4y = 8Step1: Find the intercepts.

The x-intercept is 4.

x-intercept:

2x - 4y = 82x - 4 (0) = 8

2x = 82x = 82 2x = 4

The y-intercept is -2.

y-intercept:

2x - 4y = 82 (0) - 4y = 8

-4y = 8-4y = 8 -4 4y = -2

CONFIDENTIAL 12

Step2: Graph the line.

Plot (4, 0) and (0, -2).Connect with a straight line.

0 2 4-4

2

4

-4

-2x

-2(4, 0)

(0, -2)

CONFIDENTIAL 13

B) y = 4 - x23

12

23

12

6 y = 6 4 - x Multiply both sides by 6, the LCD of the fractions, to clear the fractions.

4y = 24 - 3x

Write the equation in standard form.3x + 4y = 24

Step1: Write the equation in standard form.

Graphing Linear Equations by Using Intercepts

CONFIDENTIAL 14

.

x-intercept: y-intercept:

The x-intercept is 8.

3x + 4y = 243x + 4 (0) = 24

3x = 243x = 24 3 3x = 8

The y-intercept is 6.

3 (0) + 4y = 244y = 244y = 24 4 4y = 6

3x + 4y = 24

Step2: Find the intercepts

CONFIDENTIAL 15

Step3: Graph the line.

Plot (8, 0) and (0, 6).

Connect with a straight line.

0 4 8-8

4812

16

x-4

(8, 0)

(0, 6)

CONFIDENTIAL 16

Use intercepts to graph the line described by each equation.

Now you try!

1) -3x + 4y = -12

132) y = x - 2

CONFIDENTIAL 17

AssessmentFind the x- and y-intercepts.

1) 2)

CONFIDENTIAL 18

Find the x- and y-intercepts.

3) 4x + 2y = 16 4) 2x - 4y = 4

5) -2y = 3x - 6 6) 4y + 5x = 2y - 3x + 16

CONFIDENTIAL 19

7) To thaw a specimen stored at -25°C, the temperature of a refrigeration tank is raised 5°C every hour. The temperature in the tank after x hours can be described by the function f (x) = -25 + 5x.

a. Graph the function and find its intercepts.

b. What does each intercept represent?

CONFIDENTIAL 20

Use intercepts to graph the line described by each equation.

8) 2x + 3y = 6

9) 4x - 5y = 20

10) y = 2x + 4

CONFIDENTIAL 21

Using InterceptsA diver explored the ocean floor 120 feet below the surface

and then ascended at a rate of 30 feet per minute. The graph shows the diver’s elevation below sea level during the ascent.

0 1 2 3 4 5

-45-60

-15-30

Elev

atio

n (f

t)

time (min)

-105-120

-75-90

-135

The x-intercept is 4. It represents the time

that the diver reaches the surface or when

depth = 0.

The y-intercept is -120. It represents the

diver’s elevation at the start of the ascent

when time = 0.

Let’s reviewLet’s review

CONFIDENTIAL 22

The y-intercept is the y-coordinate of thepoint where the graph intersects the y-axis.The x-coordinate of this point is always 0.

The x-intercept is the x-coordinate of the point where the graph intersects the x-axis. The y-

coordinate of this point is always 0.

CONFIDENTIAL 23

Finding Intercepts

0 2-2-4

2

-2-4

The graph intersects the y-axis at (0, -3).

Find the x- and y-intercepts.

A)

The y-intercept is -3.

The graph intersects the x-axis at (-4, 0).The x-intercept is -4.

Next page

CONFIDENTIAL 24

The x-intercept is 4.

B) 3x - 2y = 12

To find the x-intercept, replace y with 0 and solve for x.

3x - 2y = 123x - 2 (0) = 12

3x - 0 = 12

3x = 123x = 12 3 3

x = 4

The y-intercept is -6.

To find the y-intercept, replace x with 0 and solve for y.

3x - 2y = 123 (0) - 2y = 12

0 - 2y = 12

-2y = 12-2y = 12 -2 -2

y = -6

CONFIDENTIAL 25

Travel ApplicationThe Sandia Peak Tramway in Albuquerque, New Mexico, travels a distance of about 4500 meters to the top of Sandia Peak. Its

speed is 300 meters per minute. The function f (x) = 4500 - 300x gives the tram’s distance in meters from the top of the peak after x minutes. Graph this function and find the intercepts. What does each intercept

represent?

Neither time nor distance can be negative, so choose several nonnegative values for x. Use the function to

generate ordered pairs.

x 0 2 5 10 15f(x) = 4500 - 300x 4500 3900 3000 1500 0

Next page

CONFIDENTIAL 26

Graph the ordered pairs. Connect the points with a line.

• y-intercept: 4500. This is the starting distance from the top (time = 0).

• x-intercept: 15. This the time when the tram reaches the peak (distance = 0).

Remember, to graph a linear function, you need to plot only two ordered pairs. It is often simplest to find the

ordered pairs that contain the intercepts.

CONFIDENTIAL 27

Use intercepts to graph the line described by each equation.Graphing Linear Equations by Using Intercepts

A) 2x - 4y = 8Step1: Find the intercepts.

The x-intercept is 4.

x-intercept:

2x - 4y = 82x - 4 (0) = 8

2x = 82x = 82 2x = 4

The y-intercept is -2.

y-intercept:

2x - 4y = 82 (0) - 4y = 8

-4y = 8-4y = 8 -4 4y = -2

CONFIDENTIAL 28

Step2: Graph the line.

Plot (4, 0) and (0, -2).Connect with a straight line.

0 2 4-4

2

4

-4

-2x

-2(4, 0)

(0, -2)

CONFIDENTIAL 29

B) y = 4 - x23

12

23

12

6 y = 6 4 - x Multiply both sides by 6, the LCD of the fractions, to clear the fractions.

4y = 24 - 3x

Write the equation in standard form.3x + 4y = 24

Step1: Write the equation in standard form.

Graphing Linear Equations by Using Intercepts

CONFIDENTIAL 30

.

x-intercept: y-intercept:

The x-intercept is 8.

3x + 4y = 243x + 4 (0) = 24

3x = 243x = 24 3 3x = 8

The y-intercept is 6.

3 (0) + 4y = 244y = 244y = 24 4 4y = 6

3x + 4y = 24

Step2: Find the intercepts

CONFIDENTIAL 31

Step3: Graph the line.

Plot (8, 0) and (0, 6).

Connect with a straight line.

0 4 8-8

4812

16

x-4

(8, 0)

(0, 6)

CONFIDENTIAL 32

You did a great job You did a great job today!today!