lesson 5-3 slope-intercept form. transparency 3 click the mouse button or press the space bar to...
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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