Question

Find an equation of the line that passes through the point (−1, 2) and is parallel to the line passing through the points (−2, −3) and (2, 5). (Let x be the independent variable and y be the dependent variable.)

Answer 1

y = 2x + 4

Explanation:

Find the slope m of the line passing through the 2 points using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 3) and (x₂, y₂ ) = (2, 5)

m =
`(5+3)/(2+2)` =
`(8)/(4)` = 2

Parallel lines have equal slopes, thus

y = 2x + c ← is the partial equation of the line

To find c substitute← (- 1, 2) into the partial equation

2 = - 2 + c ⇒ c = 2 + 2 = 4

y = 2x + 4 ← is the equation of the line