Question

Lana is trying to find an equation for a line that passes through (5, 2) and is parallel to 3x + 2y = 15. explain the steps that lana could take to determine the equation.

Answer 1

We have the following equation:
 3x + 2y = 15

 Step 1:
 Rewrite given equation:
 2y = 15 - 3x
 y = 15/2 - (3/2) x

 Step 2:
 Parallel lines have the same slope:
 y = mx + b
 m = -3 / 2
 y = (- 3/2) x + b

 Step 3:
 Find b, for this we evaluate the point (5, 2) in the equation:
 2 = (- 3/2) (5) + b
 2 = (- 15/2) + b
 2 + 15/2 = b
 19/2

 Step 4:
 The parallel line is:
 y = (- 3/2) x + 19/2