Question

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)?

Answer 1

First things first.  Solve the equation for y, getting it into y = mx + b form so it's easy to determine the slope.  5x + 2y = 12 so 2y = -5x + 12.  Dividing everything by 2 we get $y=- \frac{5}{2}x+6$.  So the slope is -5/2.  Parallel lines have the same slope, so we will have a slope of -5/2 in our new equation, we just have to find out what that equation is.  We have an x and a y value from the point, so we will use that, along with the slope, to find b, the y-intercept.  $4=- \frac{5}{2}(-2)+b$ and 4 = 5 + b.  So b = -1.  Now let's write the equation: $y=- \frac{5}{2}x-1$.  And there you go!