Problem 27)
The domain is {-4,-2,0,2,4}
Plug in each of those values, one at a time, for x
Plug in x = -4
y = (-1/2)*x + 1
y = (-1/2)*(-4) + 1
y = 2 + 1
y = 3
So y = 3 is part of the range
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Plug in x = -2
y = (-1/2)*x + 1
y = (-1/2)*(-2) + 1
y = 1 + 1
y = 2
So y = 2 is part of the range
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Plug in x = 0
y = (-1/2)*x + 1
y = (-1/2)*(0) + 1
y = -0 + 1
y = 1
So y = 1 is part of the range
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Plug in x = 2
y = (-1/2)*x + 1
y = (-1/2)*(2) + 1
y = -1 + 1
y = 0
So y = 0 is part of the range
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Plug in x = 4
y = (-1/2)*x + 1
y = (-1/2)*(4) + 1
y = -2 + 1
y = -1
So y = -1 is part of the range
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The range is the set {3, 2, 1, 0, -1}
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Problem 28)
Since the equation y = (-1/2)*x + 1 is in the form y = m*x+b, this means we have a linear equation.
So we only need two points to plot this line
If x = 0, then y = 1 as shown in problem 27. So the point (0,1) is on the line. This is the y intercept.
If x = 2, then y = 0 as shown in problem 27. So the point (2,0) is on the line. This is the x intercept
See the attached image to see the graph of the equation.
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Problem 29)
To find the x intercept, plug in y = 0. Then solve for x
7x - 3y = 21
7x - 3(0) = 21
7x - 0 = 21
7x = 21
7x/7 = 21/7
x = 3
The x intercept is 3 meaning that the point (3,0) is on the line.
This is where the graph crosses the x axis.
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To find the y intercept, plug in x = 0. Then solve for y
7x - 3y = 21
7(0) - 3y = 21
0 - 3y = 21
-3y = 21
-3y/(-3) = 21/(-3)
y = -7
The y intercept is -7 meaning the point (0,-7) is on the line. This is where the graph crosses the y axis.
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Problem 30)
The equation y = -3x+5 is in the form y = mx+b
m = -3 is the slope
b = 5 is the y intercept
You can write the y intercept as an ordered pair (0,5)
This is where the graph crosses the y axis
The slope of -3 means we go down 3 each time we move over to the right 1
slope = rise/run = -3/1
rise = -3
run = 1
