Lesson 5-3

Slope-Intercept Form

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Objectives

• Write and graph linear equations in slope-intercept form

• Model real world data with an equation in slope-intercept form

Vocabulary

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

y

x

y

x

x-y Coordinate Plane

Quadrants

III

III IV

Point Plotting

(x, y) (-4, 7) (5, -8)

x – left or righty – up or down

right 5

down 8

left 4

up 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:

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

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

Example 3

Graph

Step 1 The y-intercept is –7. So graph (0, –7).

Step 2 The slope is 0.5

or

From (0, –7), move up 1 unit and right 2 units. Draw a dot.

Step 3 Draw a line connecting the points.

y = 0.5x – 7

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:

Example 4 cont

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.

5x + 4y = 8

Step 2 The y-intercept of

is 2.

So graph (0, 2).

Example 5Health 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.

Example 5 cont

Variables Let R = the ideal heart rate.Let a = years older than 25.

Equation

ideal rateIdeal rate of years older for 25- rate equals change times than 25 plus year-old.

R a 117

Answer:

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.

Summary & Homework

• Summary:– 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. 275 14-32 even– Pg. 831 1-12 all