Download Chapter 4 Quiz (4

Graphing Linear Equations
Verifying Solutions of an Equation
a) Substitute the ordered pair into the equation
b) Simplify both sides of the equation
c) If the numbers are the same: the ordered pair is a solution
If the numbers are different: the ordered pair is not a solution
Examples
1) Is (1,2) a solution of x + 3y = 6?
a) 1 + 3(2) = 6
b) 7 ≠ 6
c) Not a solution
2) Is (3,-1) a solution of y = 2x – 7?
a) -1 = 2(3) – 7
b) -1 = -1
c) Solution
Try these:
Determine if the ordered pair is a solution
1) y =2x – 3 (-7, -1)
2) -4x + 3y = 1
(5,7)
Graphing with Tables from Equations
a) Rewrite the equation in the form y = mx + b (Solve for y)
b) Choose four x-values for a table
c) Plug in the x-values to find the corresponding y-values
d) Plot your points and draw a line through them
Examples
Given: y + 2 = 3x
a) y = 3x – 2
b&c)
d)
x y
-1 -5
0 -2
1 1
2 4
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Given: 2x – 2y = 6
a) -2y = -2x + 6
-2
-2
y=x–3
b&c)
x
-1
0
1
2
y
-4
-3
-2
-1
Try these:
1) y – 1 = x
x
y
d)
2) 4x + 2y = -6
x
y
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Special Equations
Graph y = 4
This graph is a horizontal line
and goes through 4 on the y axis
Graph x = -3
This graph is a vertical line
and goes through -3 on the x- axis
Horizontal Lines have zero slopes
Vertical lines have undefined slopes
or “no slope”
Try These:
What is the equation?
What is the equation?
What is the slope?
What is the slope?
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Graphs Using x and y-intercepts
x-intercept
Example:
The point where the graph crosses the x-axis
To find the x-intercept:
a) Substitute 0 for y
b) Solve for x
Given: 2x + 3y = 6
2x + 3(0) = 6
2x = 6
x=3
________________________________________________________________________
y-intercept
Example:
Given y = 3x + 1
The point where the graph crosses the y-axis
y = 3(0) + 1
To find the y-intercept:
a) Substitute 0 for x
y=1
b) Solve for y
_______________________________________________________________________
Find the x and y-intercepts of the following: y = 2x – 4 Then graph it.
x –intercept
0 = 2x – 4
y -intercept
y = 2(0) – 4
4 = 2x
y=0–4
2=x
y = -4
Try These:
Find the x and y intercept of each equation and graph the equation:
11) 3x + 5y = 15
12) y = x + 4
6) -2x + 4y = -8
x-intercept _________
y-intercept__________
x-intercept _________
y-intercept__________
x-intercept _________
y-intercept__________
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I. Determine if the ordered pair is a solution
1) y = 3x – 4 (-5, -11)
2) -6x + 5y = -6
3) 2x – 7y = -20
(-3, 2)
4) y = 12x – 4
5) 3x + 8y = -10
(-2, 7)
6) y = 4x – 10
(4,6)
(-3, -32)
(12, 38)
II. Use the equation to make a table of 3 values, then graph the line
7) y = -3x + 2
8) y = 2x – 4
x
y
x
y
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9) y – 4 = -2x
10) -6x + 3y = -15
x
x
y
y
Find the x and y intercept of each equation and graph the equation:
11) 3x + 4y = 12
12) y = x + 2
13) 2x + 5y = 10
x-intercept _________
x-intercept _________
x-intercept _________
y-intercept__________
y-intercept__________
y-intercept__________
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Special Equations
14) What is the equation?
15)What is the equation?
What is the slope?
What is the slope?
16) What is the equation?
17)What is the equation?
What is the slope?
What is the slope?
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I. Determine if the ordered pair is a solution
1) y = 3x – 4 (-5, -11)
2) -6x + 5y = -6
3) 4x – y = 1 (-1, 3)
4) 2y – 3x = 5 (4, 1)
(4,6)
5) -5x + 10y = 20 (2, 3)
II. Use the equation to make a table of 3 values, then graph the line
6) y = -3x + 2
7) y = 2x - 4
x
-1
0
1
2
y
x
y
Find the x and y intercept of each equation and graph the equation:
8) 3x + 4y = 12
9) y = x + 2
10) 2x + 5y = 10
x-intercept _________
x-intercept _________
x-intercept _________
y-intercept__________
y-intercept__________
y-intercept__________
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Practice Mini-Test
Determine if the ordered pair is a solution
1) y = -5x + 7 (6, -23)
Use the equation to make a table of 3 values,
then graph the line
3) y = -x + 2
x y
-1
0
1
2
2) -3x + 7y = -4
(4,2)
Find the x and y intercept of each
equation and graph the equation:
4) 6x – 3y = -12
x-intercept _________
y-intercept _________
5) What is the equation of the line?
7) Graph the equation x = -4
6) What is the slope of the line?
8) What is the slope of the line?
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