Question

What is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point (4, 32)?

A: y=-1/4x +33
B: y=-1/4x + 36
C: y = 4x - 16
D: y = 4x + 16

Answer 1

Option D: y = 4x + 16

Explanation:

Given the line: y - 1 = 4(x + 3) ⇒ y = 4x + 13

The slope of the given line = m = 4

The required line is parallel to the given line

So, the slope of the required line = m = 4

So, the general equation of the required line: y = 4x + c

Where c is constant represents y-intercept

To find the value of c, substitute with the point (4,32)

At x = 4 y = 32

∴ 32 = 4 * 4 + c

∴ c = 32 - 16 = 16

∴ y = 4x + 16

The answer is option D: y = 4x + 16