Question

Consider the point (−8,3) and the line 2x + 3y = 5. Find the equation of the line through the point and parallel to the given line.

Answer 1

parallel lines will have the same slope. so let's start by simplifying things

3y = -2x + 5
y = -2/3x + 5/3

Now we have the equation in the form y = mx + b, but we need to find an equation through the point that is also parallel so we'll put it in the form:

y - y1 = slope (x - x1)

y - 3 = 2/3(x + 8)

y - 3 = 2/3x + 16/3

y = 2/3x + 25/3