Transcript 2.3 Quick Graphs of Linear Equations

Warm Up
The senior class is selling tickets for a car wash to raise money for Grad
Nite. Since pickup trucks, vans, and SUVs are bigger vehicles they are
charged more than cars. Write an equation to model how much money
was raised.
What information do you need to solve the problem?
•The price cars are charged.
$4.00
•The number of cars washed. c
•The price of vans, SUVs, and trucks are charged. $6.00
•The number of vans, SUV’s, and trucks washed. t
•How much money is raised. $600.00
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On page 82 complete the investigating slope
and y-intercept
2.3: Quick Graphs of Linear Equations, p. 82
Slope-Intercept Form
y = mx + b
m = slope
b = y-intercept
Example 0 Put the following equation in slope-intercept form.
3x − 2y = 6
−3x
−3x
2y  3x  6
−2
−2
3
y x3
2
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2.3: Quick Graphs of Linear Equations, p. 82
Example 1a Graph the following linear equation using the
slope and y-intercept
2
y x2
3
1) Find the slope and y-intercept.
2
m ;
3
y
−3
b2
2) Plot the y-intercept.
3) Plot the slope.
+2
−2
+3
x
2
−2
m=
or m =
−3
3
4) Draw a line through the points.
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2.3: Quick Graphs of Linear Equations, p. 82
A. a = −40t + 1000
a = amount owed
t = time in weeks
B.
Amount Owed
Example 2 You buy a $1200 stereo on the layaway plan at your
local Wally World. You put $200 down and then make
payments of $40 a week until it’s paid off.
A. Write an equation to model the situation.
B. Graph the model. 1200
1000
800
600
400
200
5 10 15 20 25 30
Number of Weeks
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2.3: Quick Graphs of Linear Equations, p. 82
Standard Form (Ax + By = C)
The easiest method for graphing a line in Standard Form is finding the x and y-intercepts.
x-intercept = where the line crosses the x-axis
y-intercept = where the line crosses the y-axis
Example 3 Graph 3x + 2y = 6
y
x
x-intercept
(set y = 0)
y-intercept
(set x = 0)
3x + 2(0) = 6
3x = 6
x2
3(0) + 2y = 6
2y = 6
y=3
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2.3: Quick Graphs of Linear Equations, p. 82
Graphing Horizontal and Vertical Lines
Example 4 Graph y = 1 and x = −2.
y=1
Count up 1 on the y-axis.
Draw a horizontal line.
y
x = −2
Count left 2 on the x-axis.
Draw a vertical line.
y
x = −2
y=1
x
x
Horizontal Lines are
in the form y = c.
Vertical Lines are in
the form x = c.
p