Write an equation of the line that passes through the given point and is parallel to the graph of the equation

Write an equation of the line that passes through the given point and is parallel to the graph of the equation

Tutors, please sign in to answer this question.

Two lines are parallel to one another if their equations have the same slope. y=2x-8 has a slope of 2, so we can use that fact plus the given point (3,-1) to solve the problem.

Using the equation (y - y_{1}) = m (x - x_{1}), let's add in m, and our point (x_{1}, y_{1}):

y - (-1) = 2 ( x - 3 ) <-- Multipying both terms on the right by 2, and subtracting -1 on the left, we get

y + 1 = 2x - 6 <-- Subtract 1 from both sides to get y alone on the left side of the equals sign

y + 1 - 1 = 2x - 6 - 1

y = 2x - 7 <-- Same slope as the original line... you can double-check by substituting in (x_{1}, y_{1}) to make sure the equality is valid. Indeed, -1 = 2(3) - 7 = -1.