2. Lesson 3 Contents Example 1Write an Equation Given Slope and y-Intercept Example 2Write an Equation Given Two Points Example 3Graph an Equation in Slope-Intercept Form Example 4Graph an Equation in Standard Form Example 5Write an Equation in Slope-Intercept Form

3. Example 3-1a Write an equation of the line whose slope is and whose y-intercept is –6. Slope-intercept form Replace m with and b with –6. Answer:

4. Example 3-1b Write an equation of the line whose slope is 4 and whose y-intercept is 3. Answer:

5. Example 3-2a Write an equation of the line shown in the graph. Step 1You know the coordinates of two points on the line. Find the slope. Let

6. Example 3-2b Simplify. The slope is 2. Step 2The line crosses the y-axis at (0, –3). So, the y-intercept is –3. Step 3Finally, write the equation. Slope-intercept form Replace m with 2 and b with –3. Answer:The equation of the line is

7. Example 3-2c Write an equation of the line shown in the graph. Answer:

8. Example 3-3a Graph Step 1The y-intercept is –7. So graph (0, –7). Step 2The slope is 0.5 or From (0, –7), move up 1 unit and right 2 units. Draw a dot. Step 3Draw a line connecting the points. y = 0.5x – 7

9. Example 3-3b Graph Answer:

10. Example 3-4a Graph Step 1Solve for y to find the slope-intercept form. Original equation Subtract 5x from each side. Simplify. Divide each side by 4.

11. Example 3-4b Divide each term in the numerator by 4. Answer: Step 2The y-intercept of is 2. So graph (0, 2).

12. Example 3-4c Step 3The slope is From (0, 2), move down 5 units and right 4 units. Draw a dot. Step 4Draw a line connecting the points. 5x + 4y = 8

13. Example 3-4d Graph Answer:

14. Example 3-5a Health The ideal maximum heart rate for a 25-year- old who is exercising to burn fat is 117 beats per minute. For every 5 years older than 25, that ideal rate drops 3 beats per minute. Write a linear equation to find the ideal maximum heart rate for anyone over 25 who is exercising to burn fat. WordsThe rate drops 3 beats per minute every 5 years, so the rate of change isbeats per minute each year. The ideal maximum heart rate for a 25-year-old is 117 beats per minute.

15. Example 3-5b VariablesLet R = the ideal heart rate. Let a = years older than 25. Equation ideal rate Ideal rate ofyears older for 25- rateequalschangetimes than 25plusyear-old. Ra117 Answer:

16. Example 3-5c Graph the equation. The graph passes through (0, 117) with a slope of Answer:

17. Example 3-5d Find the ideal maximum heart rate for a person exercising to burn fat who is 55 years old. The age 55 is 30 years older than 25. So, Ideal heart rate equation Replace a with 30. Simplify. Answer:The ideal heart rate for a 55-year- old person is 99 beats per minute.

18. Example 3-5e 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. a.Write a linear equation to find the average amount spent for any year since 1986. Answer:where D is the amount of money spent in millions of dollars, and n is the number of years since 1986

19. Example 3-5f 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. b.Graph the equation. Answer:

20. Example 3-5g 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. c.Find the amount spent by consumers in 1999. Answer:$4.95 million

21. End of Lesson 3