What is an equation of the line that passes through the point (-2,-4) and is parallel to the line 5x-2y=6?
Long way: find the slope of the original line and use the point-slope form:
Original line: 5x - 2y = 6
solve for y: -2y = -5x + 6
y = (5/2)x - 3
slope = 5/2
Use point-slope form to find the equation of the new line:
y - y1 = m(x - x1)
---> y - -4 = (5/2)·(x - -2)
y + 4 = (5/2)(x + 2)
y + 4 = (5/2)x + 5
y = (5/2)x + 1
Rewriting: 2y = 5x + 2 (multiplied both sides by 2)
-5x + 2y = 2
5x - 2y = -2
Short way: notice that the old equation 5x - 2y = 6 and the new equation 5x - 2y = -2
have the same coefficients of the x-term and the y-term and their only difference is the constant.
So, to find the new equation, start with 5x - 2y =
and put in the point (-2, -4) and solve: 5(-2) - 2(-4) = -10 + 8 = -2
This will give us the new constant, so the new equation is 5x - 2y = -2