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Question

What is the equation of the line that passes through the point (-8,-3) that is parallel to the line 5x-8y=-40?

Answer 1

All parallel lines have the same slope, so we first want to put the equation of the line in the question into slope-intercept form (y=mx+b) to find the slope. We do this by solving for y in the equation:

5x-8y=-40

8y = 5x + 40

y = 5/8 x + 5

This tells us that the slope is 5/8.

Next, we use point-slope form to find the equation of the parallel line.

y-y₁ = m(x-x₁), which gives us the equation of a line with slope m and passes through the point (x₁, y₁)

y-(-3) = 5/8(x-(-8))

y+3 = 5/8x + 5

y=5/8x + 2

Answer 2

5x-8y =-40

solve any linear equation for y and the x term's coefficent is the slope

8y=5x-40

y = (5/8)x -5 slope of any parallel has the same slope = 5/8

y=mx + b where m=5/8, plug in x=-8, y =-3 to solve for b, the y intercept

-3 =(5/8)(-8) + b

b= -3 +5 = 2

y= 5x/8 + 2 is the parallel line throught the point (-8,-3)