Answer: D) y = 4x+4
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Step-by-step explanation:
The given visual line has a slope of -1/4. We can see this by starting at (0,2) and we do two things
a) move down 1
b) move over to the right 4
This leads to slope = rise/run = -1/4
Once we find the slope of the original line, we take the opposite reciprocal. This is also called the negative reciprocal. So we'll take the reciprocal of -1/4 to get -4/1 or just -4. Then we flip from negative to positive.
In short we flip the fraction and the sign. That has us go from -1/4 to 4.
The original slope is -1/4. The perpendicular slope is 4.
Side note: multiplying any two perpendicular slopes leads to -1. Neither line can be vertical.
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So we found the slope of the perpendicular line to be m = 4.
We don't know which point the perpendicular line goes through, so theoretically we have infinitely many equations to pick from. They are all in the form y = 4x+b. Note how I replaced m in y = mx+b with 4.
So our answer will be in the form y = 4x+b. Choices A through C don't fit the description. Only choice D does. So choice D is the answer.
With y = 4x+4, the slope is 4 and the y intercept is 4.