Question

Describe and correct the error the student made when writing the equation of the line that passes through ​(​-8,5) and is perpendicular to y = 4x+2.

Answer 1

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

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=-1/4(x-(8))

y-5=1/4(x+8)

y-5=1x/4-2

y=-1x/4-2+5

y=-1x/4+3

is the 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))

So Option D

Answer 2

Using the slope - intercept relation, the equation of the perpendicular line which passes through (-8, 5) is ; $\frac{-1}{4}x + 3$

Given the slope - intercept relation :

• y = 4x + 2

Slope of the line = 4

Since, the line is perpendicular ; the slope of the line passing through it will be the negative reciprocal ;

Negative Reciprocal of 4 = $\frac{-1}{4}$

Using the points (-8, 5) ; we obtain the intercept, c :

x = -8 ; y = 5

5 = -1/4(-8) + c

5 = 2 + c

c = 5 - 2

c = 3

Hence, the equation of the perpendicular line is ; $\frac{-1}{4}x + 3$

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