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Answer:

y = 4x+17,   or choice #3

Step-by-step explanation:

The slope of the line given is -1/4. The slope of a line perpendicular to the original line has a slope that is the negative reciprocal of -1/4, which is 4. The product of the perpendicular and the original slope must be -1, so to check: 4*(-1/4)=-1.

So far we have y = 4x+b for the perpendicular line. The bias b can be determined using the point given, (-3,5):

5 = 4(-3) + b ==> b = 17

Therefore, the equation of the line perpendicular to the line given is:

y = 4x+17,   or choice #3

Answer:

y = 4x + 17

Step-by-step explanation:

We are to write an equation of the line that is perpendicular to line whose equation is y = [tex]\frac{1}{4}[/tex] and whose slope is -[tex]\frac{1}{4}[/tex] = 4

And passes through (-3.5)

The product of slopes of two perpendicular lines is -1

So the slope of the line we are to find is -1 ÷ -[tex]\frac{1}{4}[/tex] = 4

Taking a point (x,y) on the line we are to find

Slope(m) = Change in y-axis ÷ Change in x-axis

Slope is [tex]\frac{y - 5}{x + 3}[/tex] = 4

Cross multiplying gives;

y - 5 = 4x + 12

Simplifying gives the equation of our second line;

y = 4x + 17

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