Section 11.4 The Slope-Intercept Form of a Linear Equations

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2
Graphs of Linear
Equations and
Inequalities in Two
Variables
11

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1. Use the slope-intercept form of the equation
of a line.
2. Graph a line given its slope and a point on
the line.
3. Write an equation of a line given its slope
and any point on the line.
4. Find an equation of a line that fits a data
set.
Objectives
11.4 Slope-Intercept Form of a Linear
Equation

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Slope-Intercept Form
The slope-intercept form of the equation of a line with
slope m and y-intercept (0, b) is
y = mx + b.
Slope (0, b) is the
y-intercept.
Use the Slope-Intercept Form

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Example
Identify the slope and y-intercept of the line with each
equation.
a. y = –4x + 1
Slope = –4 and y-intercept = (0, 1)
b. y = 6x
can be written as y = 6x + 0
Slope = 6 and y-intercept = (0, 0)
Identifying Slopes and y-Intercepts

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Graphing a Line by Using the Slope and y-intercept
Step 1 Write the equation in slope-intercept form, if
necessary, by solving for y.
Step 2 Identify the y-intercept. Plot the point (0, b).
Step 3 Identify slope m of the line. Use the geometric
interpretation of slope (“rise over run”) to find
another point on the graph by counting from the
y-intercept.
Step 4 Join the two points with a line to obtain the
graph.
Graph a Line Given Its Slope and a Point on the Line

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Example
Graph
Step 1 The equation is in slope-intercept form.
m = 2/3
y-intercept = (0, –1)
Graphing Lines Using Slopes and y-Intercepts
Step 2 The y-intercept is (0, –1) . Graph this point.
2
1
3
y x 

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Example (cont)
Graph
Graph a Line Given Its Slope and a Point on the Line
Step 4 Connect the two points.
Step 3 The slope is 2/3.
2
1
3
y x 
rise 2
run 3

Count up 2 units and to the
right 3 units.

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Example
Write an equation in slope-intercept form of the line passing
through the given point and having the given slope.
m = –4 and y-intercept (0, 9)
Here m = –4 and b = 9, so an equation is
Using Slope-Intercept Form to Write Equations of Lines
y = mx + b
y = –4x + 9

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Example
Graph each line passing through the given point
and having the given slope.
(a) (4, –2), m = 0
Recall that a horizontal line has slope 0.
To graph this line, plot the point (4, –2)
and draw the horizontal line through it.
Graphing Horizontal and Vertical Lines Using Slope
and a Point

10. Slide - 10Copyright © 2018, 2014, 2010 Pearson Education Inc.A L W A Y S L E A R N I N G
Example (cont)
Graph each line passing through the given point
and having the given slope.
(b) (2, –4), undefined slope
A vertical line has undefined slope.
To graph this line, plot the point
(2, –4) and draw the vertical line
through it.
Graphing Horizontal and Vertical Lines Using Slope
and a Point