Question

A line passes through the point (2,-2) and is parallel to the line y = 3x + 4. What is its equation?

3 points
y = 3x - 8
8x + 3y = 23
5x + y = 23
y = 8x - 3
Other:

Answer 1

y = 3x - 8

Explanation:

Parallel lines have the same slope, while perpendicular lines have negative reciprocal slopes

In order to find a line parallel to y = 3x + 4, we will need to use the same slope, 3.

We can use the point-slope formula y - y₁ = m(x - x₁) where we have our (x₁, y₁) point (2, -2)

Now we just need to plug in our values to solve for the equation of a line

• y - (-2) = 3(x - (2))

Distributing the negative to the -2 and the 3 to the (x - 2) we get:

• y + 2 = 3x - 6

Now subtracting 2 from both sides we get

• y = 3x - 8

Now since this equation is in the form y = mx + b, nothing further needs to be done and this is the parallel line to the line y = 3x + 4