Question

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?

Answer 1

First let’s put 5x+2y = 12 into slope-intercept form.

2y = -5x + 12

y = (-5/2)x + 6

So any line that is parallel to y = (-5/2)x + 6 must have a slope of -5/2.

Our answer then is y = (-5/2)x + c

Now all that remains is to find out the value of c.

We know this line passes through the point (-2,4). Which means when x = -2, y = 4.

4 = (-5/2)(-2) + c

4 = 5+c

c = -1

Hence the line you want is y = (-5/2)x - 1

Since the question gave the line in standard form and didn’t ask for any particular form, let’s give the answer in the same form that the question asked.

2y = -5x - 2

5x + 2y = -2