Question

A line passes through the point (–3, 4) and its y-intercept is (0, –2). What is the equation of the line that is parallel to the given line and passes through the point (–5, 2)?

Answer 1

y = - 2x - 8

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 4) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m =
`(-2-4)/(0+3)` =
`(-6)/(3)` = - 2

• Parallel lines have equal slopes, hence slope of parallel line = - 2, thus

y = - 2x + c ← partial equation of parallel line

To find c substitute (- 5, 2) into the partial equation

2 = 10 + c ⇒ c = 2 - 10 = - 8

y = - 2x - 8 ← equation of parallel line