Write the equation of the line which passes through (3, –4) and is perpendicular to the line with equation 4y – x = 1.

Question

Select one:
a. 4x + y = 8
b. 4x – y = 3
c. x + 4y = –4
d. x – 4y = 8

Answer 1

Hi Rachelle,

 

To solve this problem, you need to know that when two lines are perpendicular to each other, their slopes have a special relationship. This is how:

If one of the lines has slope m₁, the other line will have a slope m₂=-1/m₁ (This is called the inverse reciprocal in mathematical jargon).

 

Let's find the slope of the given line 4y – x = 1

We need to write it in he form y = mx+b so

4y = x+1

y = (x+1)/4 or x/4 + 1/4

we can see that the slope of this line is 1/4.

 

Now, we know that the line perpendicular to this line will have a lope of

-1*(1/(1/4)) according to the inverse reciprocal relationship

so we end up with slope -4

We also know a point where this line passes through, A(3,-4)

According to y = mx+b do you think you figure out the rest to find the equation of the line?

I will tell you that the answer is A.