(3,-1); y= 2x-8

Question

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

 

Answer 1

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 - y₁) = m (x - x₁), let's add in m, and our point (x₁, y₁):

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 (x₁, y₁) to make sure the equality is valid.  Indeed, -1 = 2(3) - 7 = -1.