<h3>
Answer: B) y = -x</h3>
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Work Shown:
g(x) = x^2-2
g(-2) = (-2)^2-2
g(-2) = 2
Saying (-2, g(-2)) is the same as saying (-2, 2)
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g(x) = x^2-2
g(1) = 1^2 - 2
g(1) = -1
Saying (1, g(1)) is the same as saying (1, -1)
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Let's find the slope of the line through (-2,2) and (1,-1)
m = (y2 - y1)/(x2 - x1)
m = (-1-2)/(1-(-2))
m = (-1-2)/(1+2)
m = -3/3
m = -1
Now turn to point slope form to find the equation
y - y1 = m(x - x1)
y - 2 = -1(x - (-2))
y - 2 = -(x + 2)
y - 2 = -x - 2
y-2+2 = -x-2+2 ... add 2 to both sides
y = -x
You could use the other point (1,-1) and you'd get the same answer. The slope m = -1 is the same each time.
