Dtermine the equation of the line that is parallel to the given line through the given point. Y= -5x+1; (-2,3)

Answer 1

Parallel lines have the same slope.

y - y₁ = m(x - x₁)

y - 3 = -5(x - (-2))

y - 3 = -5(x + 2)

y - 3 = -5x - 10

y = -5x - 7

Answer 2

You're given the equation of a line in slope-intercept format so you know the slope of the parallel line is -5. What you have to figure out is the Y-intercept or where the line crosses the Y-axis. For the given line, that's +1. So start with Y = mX + b, fill in what you know, solve for b, and rewrite. Using the X and Y values of the given point, we get:

3 = (-5)(-2) + b, 3 = 10 + b, b = -7

Now we rewrite as:

Y = -5X - 7