What is the equation of line j?

Question

Line g is represented by the equation y=-4/5x+1. Line j is the equation perpendicular to line g and passes through the point (-10,0).

Answer 1

Just like the previous problem, we're going to need the point-slope formula for this line. Before that, though, we need to figure out the slope.

The problem tells us that the line is perpendicular which means that we need the negative reciprocal of the original line. To find the neg-recip, we flip the sign negative ⇔ positive and flip the numerator and denominator.

The original slope is negative, so we make it positive, and by flipping the 4/5 part, we now have 5/4.

 

Now that we have our slope, we use the point-slope formula to find line j:

y - y₁ = m(x - x₁)

y - 0 = 5/4(x - (-10))

y = 5/4(x + 10)

y = ⁵/₄x + ⁵⁰/₄

y = ⁵/₄x + ²⁵/₂