write the equation of a parallel line to y=-5/4x+7 that passes through the point (-4,1)

Question

write the equation of a parallel line to y=-5/4x+7 that passes through the point (-4,1)

Answer 1

The parallel line of y=-5/4x+7 that passes through point (-4,1) is y=-5/4x-4.

To begin, we know that parallel lines have to have the same slope so they don't intersect each other. Luckily for us, that means the only thing we need to change about our equation is the y-intercept (the b value in y = mx+b).

So, let's take our original equation with the same slope and rewrite it using point slope form:

y-y₁=-5/4(x-x₁)

Our point (x₁,y₁) will come from the problem, (-4,1). Substitute that information:

y-1=-5/4(x-(-4))

y-1=-5/4(x+4)

Now we can distribute the -5/4 and add 1 to the right to get our final slope-intercept form:

y-1=-5/4x-5

y=-5/4x-4.

The parallel line of y=-5/4x+7 that passes through point (-4,1) is y=-5/4x-4.