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