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5-2 Using Intercepts

Warm Up 1. 5x + 0 = –10 Solve each equation.

2. 33 = 0 + 3y

3.

4. 2x + 14 = –3x + 4

5. –5y – 1 = 7y + 5


1. The student is able to find x and y-intercepts

2. The student is able to identify meanings of x and y-intercepts.

3. The student is able to use x and y-intercepts to graph an equation

Learning Goals

5-2 Using Intercepts The y-intercept is the y-coordinate of the point 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.

5-2 Using Intercepts Example 1: Finding Intercepts

A.

Find the x- and y-intercepts.

Then write them as ordered pairs

The y-intercept is___

The x-intercept is___





(__,__) (__,__)

B. C.

(__,__) (__,__) (__,__) (__,__)

5-2 Using Intercepts Example 1: Finding Intercepts

a.


Then write them as ordered pairs







b. c.

(__,__) (__,__) (__,__) (__,__) (__,__) (__,__)


Example 1B: Finding Intercepts

A. 5x – 2y = 10 To find the y-intercept, replace x with 0 and solve for y.

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



Example 1B: Finding Intercepts

A. 5x – 2y = 10 Find the x- and y-intercepts.


Find the x- and y-intercepts. B. –3x + 5y = 30

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



Find the x- and y-intercepts. B. –3x + 5y = 30


Find the x- and y-intercepts. a. 4x + 2y = 16 b. 3x - 2y = 12


Find the x- and y-intercepts. a. 4x + 2y = 16







b. 3x - 2y = 12

5-2 Using Intercepts Example 2: Sports Application A. Trish can run the 200 m dash in 25 s.

The function f(x) = 200 – 8x gives the distance remaining to be run after x seconds. Graph this function and find the intercepts. What does each intercept represent?

f(x) = 200 – 8x

x

The x-intercept represents____________________

The y-intercept represents____________________


a. The school 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.

2x + 3y =60

x




b. The 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.

f(x)=4500-300x

x




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.

Helpful Hint You can use a third point to check your line. Either choose a point from your graph and check it in the equation, or use the equation to generate a point and check that it is on your graph.

5-2 Using Intercepts Example 3A: Graphing Linear Equations by Using

Intercepts Use intercepts to graph the line described by the equation. A. 3x – 7y = 21

x-intercept: y-intercept:


Intercepts Use intercepts to graph the line described by the equation.


B. y = –x + 4



x-intercept: y-intercept: C. –3x + 4y = –12




a. 2x - 4y = 8




y = 13x − 2b.




c. 5x - 10y = 20


Lesson Quiz: Part I 1. An amateur filmmaker has $6000 to make a film

that costs $75/h to produce. The function f(x) = 6000 – 75x gives the amount of money left to make the film after x hours of production. Graph this function and find the intercepts. What does each intercept represent?


Lesson Quiz: Part II 2. Use intercepts to graph the line described by

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