Find an equation of the line that passes through the point (−1, 7) and is parallel to the line passing through the points (−2, −3) and (2, 5).

Answer 1

y = 2x + 9

Use the two points on the given line (-2,-3), and (2,5) to calculate the slope, m and the equation of the given line in Slope Intercept Form

y = mx + b

Let your first point be (-2,-3) and your second point be (2,5)

m = (y₁ - y₂)/(x₂ - x₁)

m = (5 -(-3))/(2-(-2)) = 8/4 =2

Parallel lines have the same slope

The given line is

y = 2x + b

5 = 2(2) + b

5 = 4 + b

5 - 4 = b

1 = b

y = 2x + 1

The Parallel line is

7 = 2(-1) + b

7 = -2 + b

7 + 2 = b

9 = b

y = 2x + 9

I hope this helps