Option D (The student should have used as the slope of the perpendicular line.) is correct.
Step-by-step explanation:
We need to identify the error that the student made in finding equation of the line that passes through (-8,5) and is perpendicular to y = 4x + 2
The slope of the required line would me -1/m because both lines are perpendicular.
So, slope of new line will be: -1/4
because the equation of slope-intercept form is:
where m is the slope
Now, for finding equation the student used point slope form i.e ![y-y_1=m(x-x_1)](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29)
where y_1 and x_1 are the points and m is the slope.
Putting values:
x_1=-8, y_1=5 and m=-1/4
![y-5=-\frac{1}{4}(x-(-8))\\y-5=-\frac{1}{4}(x+8)\\y-5=-\frac{1x}{4}-2\\y=-\frac{1x}{4}-2+5\\y=-\frac{1x}{4}+3](https://tex.z-dn.net/?f=y-5%3D-%5Cfrac%7B1%7D%7B4%7D%28x-%28-8%29%29%5C%5Cy-5%3D-%5Cfrac%7B1%7D%7B4%7D%28x%2B8%29%5C%5Cy-5%3D-%5Cfrac%7B1x%7D%7B4%7D-2%5C%5Cy%3D-%5Cfrac%7B1x%7D%7B4%7D-2%2B5%5C%5Cy%3D-%5Cfrac%7B1x%7D%7B4%7D%2B3)
This is the correct solution.
The student made error by using the wrong slope he used 2 instead of -1/4
in the step ![y-5 = 2(x-(-8))](https://tex.z-dn.net/?f=y-5%20%3D%202%28x-%28-8%29%29)
So, Option D (The student should have used as the slope of the perpendicular line.) is correct.
Keywords: Equation of line using Slope
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