1. Graphing Equations in Slope- Intercept Form (4-1) Objective: Write and graph linear equations in slope-intercept form. Model real-world data with equations in slope-intercept form.

2. Slope-Intercept Form An equation of the form y = mx + b, where m is the slope and b is the y-intercept, is in slope-intercept form. The variables m and b are called parameters of the equation. Changing either value changes the equation’s graph.

3. Key Concept The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Example: y = mx + b y = 2x + 6 slopey-intercept

4. Example 1 Write an equation in slope-intercept form of the line with a slope of ¼ and a y-intercept of -1. Then graph the equation. m = ¼ b = -1 y = mx + b y = ¼ x – 1 Plot -1 on the y-axis. Use ¼ as rise over run to find more points.

5. Graphing Equations in Slope- Intercept Form When an equation is not written in slope- intercept form, it may be easier to rewrite it before graphing.

6. Example 2 Graph 5x + 4y = 8. Solve for y. m = - 5 / 4 b = 2 5x + 4y = 8 -5x 4y = -5x + 8 4 4 4 y = - 5 / 4 x + 2

7. Horizontal Lines Horizontal lines have a slope of 0. They are graphs of constant functions, which can be written in slope-intercept form as y = 0x + b, or y = b, where b is any number. Constant functions do not cross the x-axis. Their domain is all real numbers, and their range is b.

8. Example 3 Graph y = -7. m = 0 b = -7 Plot -7 on the y-axis. Horizontal lines have a slope of 0.

9. Vertical Lines Vertical lines have undefined slope. So, equations of vertical lines cannot be written in slope-intercept form.

10. Write an Equation from the Graph There are times when you will need to write an equation when given a graph. To do this, locate the y-intercept and use the rise and run to find another point on the graph. Then write the equation in slope-intercept form.

11. Example 4 Which of the following is an equation in slope-intercept form for the line shown in the graph? A.y = - ½ x + 3 B.y = 2x – 3 C.y = ½ x + 3 D.y = -2x – 3 b = -3 m = 2 / 1 = 2 y = mx + b

12. Modeling Real-World Data Real-world data can be modeled by a linear equation if there is a constant rate of change. The rate of change represents the slope. The y-intercept is the point where the value of the independent variable is 0.

13. Example 5 The ideal maximum heart rate for a 25-year- old exercising to burn fat is 117 beats per minute. For every five years older than 25, that ideal rate drops three beats per minute. a.Write a linear equation to find the ideal maximum heart rate for anyone over 25 who is exercising to burn fat. m = - 3 / 5 b = 117 y = - 3 / 5 x + 117

14. Example 5 b.Graph the equation. y = - 3 / 5 x + 117 Plot 117 on the y-axis. Use - 3 / 5 as rise over run.

15. Example 5 c.Find the ideal maximum hear rate for a 55- year-old person exercising to burn fat. 55 is 30 years over 25, so let x = 30. y = - 3 / 5 x + 117 y = - 3 / 5 (30) + 117 y = -18 + 117 y = 99 beats per minute

16. Check Your Progress Choose the best answer for the following. Write an equation in slope-intercept form of the line whose slope is 4 and whose y-intercept is 3. A.y = 3x + 4 B.y = 4x + 3 C.y = 4x D.y = 4 m = 4 b = 3 y = mx + b

17. Check Your Progress Choose the best answer for the following. Graph 3x + 2y = 6. A.B.C.D. 3x + 2y = 6 -3x 2y = -3x + 6 2 2 2 y = - 3 / 2 x + 3

18. Check Your Progress Choose the best answer for the following. Graph 5y = 10. A. B.C. D. 5y = 10 5 y = 2

19. Check Your Progress Choose the best answer for the following. Which of the following is an equation in slope- intercept form for the line shown in the graph. A.y = - 1 / 3 x + 3 B.y = 1 / 3 x – 1 C.y = -3x + 1 D.y = 3x – 1 b = 1 m = - 3 / 1 = -3 y = mx + b

20. Check Your Progress Choose the best answer for the following. A.The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. Write a linear equation to find the average amount D spent for any year n since 1986. A.D = 0.15n B.D = 0.15n + 3 C.D = 3n D.D = 3n + 0.15 m = 0.15 b = 3

21. Check Your Progress Choose the best answer for the following. B.The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. Find the amount spent by consumers in 1999. A.$5 million B.$3 million C.$4.95 million D.$3.5 million 1999 – 1986 = 13 years Let n = 13 years D = 0.15n + 3 D = 0.15(13) + 3 D = 1.95 + 3