1. Lesson 5-3
Slope-Intercept Form

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Transparency 3

3. Transparency 3a

4. Objectives Write and graph linear equations in slope-intercept form
Model real world data with an equation in slope-intercept form

5. Vocabulary
Slope-intercept form - an equation of the form y = mx + b, where m is the slope and b is the y-intercept

6. x-y Coordinate Plane Point Plotting Quadrants II I III IV
up 7
left 4
right 5
III IV
down 8
(x, y) (-4, 7) (5, -8)
x – left or right
y – up or down

7. Example 1
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:

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

9. Example 2 cont Simplify. The slope is 2.
Step 2 The line crosses the y-axis at (0, –3). So, the y-intercept is –3.
Step 3 Finally, write the equation.
Slope-intercept form
Answer: The equation of the line is

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

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

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

13. Example 5
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.
Words The rate drops 3 beats per minute every 5 years, so the rate of change is beats per minute each year. The ideal maximum heart rate for a 25-year-old is 117 beats per minute.

14. Example 5 cont Variables Let R = the ideal heart rate.
Let a = years older than 25.
Equation
ideal rate Ideal rate of years older for 25- rate equals change times than 25 plus year-old. R a
117
Answer:

15. Example 5 cont
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.

16. Summary & Homework Summary: Homework:
The linear equation y = mx + b is written in slope-intercept form, where m is the slope, and b is the y-intercept
Slope-intercept form allows you to graph an equation quickly
Homework:
Pg even
Pg all
In almost all the chapter summaries of ch.5 there’s a graph!