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Graph a Function Using Intercepts

Learn how to graph a function using x and y intercepts. Find the intercepts, plot the points, and connect them to graph the function.

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Graph a Function Using Intercepts

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  1. Lesson Menu Main Idea and New Vocabulary Example 1: Graph a Function Using Intercepts Example 2: Graph a Function Using Intercepts Example 3: Using Intercepts Example 4: Using Intercepts

  2. Graph a function using the x- and y-intercepts. • standard form • x-intercept Main Idea/Vocabulary

  3. Graph a Function Using Intercepts State the x- and y-intercepts of the function 2x − 3y = 6. Graph the function. Step 1Find the x-intercept. To find the x-intercept, let y = 0. 2x – 3y= 6 Write the equation. 2x – 3(0)= 6 Replace y with 0. 2x = 6 Simplify. x = 3 Divide each side by 2. The x-intercept is 3. Example 1

  4. Graph a Function Using Intercepts Step 2Find the y-intercept. To find the y-intercept, let x = 0. 2x– 3y = 6 Write the equation. 2(0)– 3y = 6 Replace x with 0. –3y = 6 Simplify. y = –2 Divide each side by –3. The y-intercept is –2. Example 1

  5. Graph a Function Using Intercepts Step 3Graph the points (3, 0) and (0, –2) on a coordinate plane. Then connect the points. Answer: Example 1

  6. A.x-intercept: 1; y-intercept: 4 B.x-intercept: –1; y-intercept: 4 C.x-intercept: 1; y-intercept: –4 D.x-intercept: –1; y-intercept: –4 State the x- and y-intercepts of the function –4x + y = 4. Graph the function. Example 1 CYP

  7. State the x- and y-intercepts of the function x + y = –3. Graph the function. Graph a Function Using Intercepts Step 1 Find the x- and y-intercepts. x-intercept y-intercept Example 2

  8. Graph a Function Using Intercepts The x-intercept is –6. The y-intercept is –3. Step 2Graph the points (–6, 0) and (0, –3) on a coordinate plane. Then connect the points. Answer: Example 2

  9. A.x-intercept: –4; y-intercept: 3 B.x-intercept: 4; y-intercept: 3 C.x-intercept: –3; y-intercept: 4 D.x-intercept: –3; y-intercept: –4 State the x- and y-intercepts of the function 3x – 4y = –12. Graph the function. Example 2 CYP

  10. Using Intercepts SCHOOL PLAY The drama department sold $1,260 worth of tickets to a play. Student tickets x cost $5 and adult tickets y cost $9. This can be represented by the function 5x + 9y = 1,260. Use the x- and y-intercepts to graph the function. x-intercept 5x + 9y= 1,260 5x + 9(0)= 1,260 5x = 1,260 x = 252 y-intercept 5x + 9y= 1,260 5(0)+ 9y= 1,260 9y = 1,260 y = 140 Example 3

  11. Using Intercepts Answer: The x-intercept is 252. The y-intercept is 140. Example 3

  12. A. C. B. D. MUSIC The Taylor family bought tickets to an outdoor concert by the school band. The cost of a student ticket is $3 and the cost of an adult ticket is $4. They spent a total of $36. This can be represented by the function 3x + 4y = 36. Use the x- and y-intercepts to graph the function. Example 3 CYP

  13. Using Intercepts SCHOOL PLAY The drama department sold $1,260 worth of tickets to a play. Student tickets x cost $5 and adult tickets y cost $9. This can be represented by the function 5x + 9y = 1,260. Interpret the x- and y-intercepts. Example 4

  14. Using Intercepts Answer: The x-intercept is the point (252, 0). This means that 252 student tickets and 0 adult tickets could be sold for the drama department to sell $1,260 worth of tickets. The y-intercept is the point (0, 140). This means that 0 student tickets and 140 adult tickets could be sold for them to sell $1,260 worth of tickets. Example 4

  15. MUSIC The Taylor family bought tickets to an outdoor concert. The cost of a student ticket is $3 and the cost of an adult ticket is $4. They spent a total of $36. This can be represented by the function 3x + 4y = 36. Which statement is true? A.The y-intercept is the point (12, 0). This means that 12 adult tickets and 0 student tickets could be sold for $36. B.The y-intercept is the point (9, 0). This means that 9 student tickets and 0 adult tickets could be sold for $36. C.The x-intercept is the point (9, 0). This means that 9 student tickets and 0 adult tickets could be sold for $36. D.The x-intercept is the point (12, 0). This means that 12 student tickets and 0 adult tickets could be sold for $36. Example 4 CYP

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