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LESSON
8.5 Slope-Intercept Form
The graph of y = 2x + 3 is shown. You can
see that the line’s y-intercept is 3, and the
line’s slope m is 2:
rise
2
m = run = 1 = 2
Notice that the slope is equal to the coefficient of x in the equation
y = 2x + 3. Also notice that the y-intercept is equal to the constant
term in the equation. These results are always true for an equation
written in slope-intercept form.
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LESSON
8.5 Slope-Intercept Form
Slope-Intercept Form
Words
A linear equation of the form y = mx + b is said to
be in slope-intercept form. The slope is m and
the y-intercept is b.
Algebra
y = mx + b
Numbers
y = 2x + 3
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LESSON
8.5 Slope-Intercept Form
EXAMPLE
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Identifying the Slope and y-Intercept
Identify the slope and y-intercept of the line with the given equation.
3x + 5y = 10
SOLUTION
Write the equation 3x + 5y = 10 in slope-intercept form by solving for y.
3x + 5y = 10
Write original equation.
5y = –3x + 10
3
y = – 5x + 2
ANSWER
Subtract 3x from each side.
Multiply each side by
1
.
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The line has a slope of – 3 and a y-intercept of 2.
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LESSON
8.5 Slope-Intercept Form
EXAMPLE
2
Graphing an Equation in Slope-Intercept Form
Graph the equation y = – 2 x + 4.
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1
The y-intercept is 4, so plot the point (0, 4).
2
The slope is – 2 = –2 .
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3
Starting at (0, 4), plot another point by
moving right 3 units and down 2 units.
3
Draw a line through the two points.
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LESSON
8.5 Slope-Intercept Form
Real-Life Situations In a real-life problem involving a linear equation,
the y-intercept is often an initial value, and the slope is a rate of change.
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LESSON
8.5 Slope-Intercept Form
EXAMPLE
3
Using Slope and y-intercept in Real Life
Earth Science The temperature at Earth’s surface
averages about 20˚C. In the crust below the surface, the
temperature rises by about 25˚C per kilometer of depth.
Write an equation that approximates the temperature
below Earth’s surface as a function of depth.
SOLUTION
Let x be the depth (in kilometers) below Earth’s surface, and let y be the
temperature (in degrees Celsius) at that depth. Write a verbal model. Then
use the verbal model to write an equation.
Temperature
Temperature
Rate of change
Depth
=
+
•
below surface
at surface
In temperature
below surface
y = 20 + 25x
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LESSON
8.5 Slope-Intercept Form
Parallel and Perpendicular Lines There is an important relationship between
the slopes of two nonvertical lines that are parallel or perpendicular.
Slopes of Parallel and Perpendicular Lines
Two nonvertical parallel
lines have the same slope.
For example, the parallel
lines a and b below both
have a slope of 2.
a || b
Two nonvertical
perpendicular lines, such as
lines a and c below, have
slopes that are negative
reciprocals of each other.
a c
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LESSON
8.5 Slope-Intercept Form
EXAMPLE
4
Finding Slopes of Parallel and Perpendicular Lines
Find the slopes of the lines that are parallel and perpendicular to the
line with equation 4x + 3y = –18.
SOLUTION
First write the given equation in slope-intercept form.
4x + 3y = –18
Write original equation.
3y = –4x – 18
y = –4x – 6
3
Subtract 4x from each side.
1
Multiply each side by 3 .
The slope of the given line is – 4 . Because parallel lines have the same slope,
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the slope of a parallel line is also – 4 . The slope of a perpendicular line is the
3
4
3
negative reciprocal of – , or .
3
4
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