Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y = -1/4 (x) + 3; (-3, 5)

A. y = -3x -5
B. y = 1/4 x -6
C. y = 4x + 17
D. y = 4x + 5

Answer 1

Slope of the given line = -1/4

Slope of line perpendicular to given line = 4

Using the slope m=4, and the point (-3,5) we can write the equation using point slope form as:

y - 5 = 4(x + 3)

y = 4x + 12 + 5

y = 4x + 17

So the correct option is C

Answer 2

Answer:
y = 4x + 17

Explanation:
The general form of the linear equation is:
y = mx + c
where:
m is the slope
c is the y-intercept

1- getting the slope:
For two lines to be perpendicular, the product of their slopes should be -1.
The given line : y = -1/4 x + 3 has slope = -1/4
This means that the slope of the line we are looking for is 4
The equation of the line now is:
y = 4x + c

2- getting the y-intercept:
To get the value of the c, we will simply use the given point, substitute in the equation and solve for c as follows:
y = 4x + c
5 = 4(-3) + c
5 = -12 + c
c = 17

Based on the above, the equation of the line is:
y = 4x + 17

Hope this helps :)