Question

A line passing through the point (12, –5) has a slope of One-third.

Complete the work shown:

1. Substitute known values for m, x1, and y1:

2. Distribute the slope through the parentheses:

3. Distribute the slope through the parentheses:

4. Solve for the y-variable:

y minus (negative 5) = one-third (x minus 12). Y + 5 = one-third (x minus 12). Y + 5 = one-third x minus 4.

y = one-third x

Answer 1

1. Substitute known values for m, x1, and y1:
y − (−5) = (1/3)(x − 12)

2. Distribute the slope through the parentheses:
y + 5 = (1/3)x − (1/3)·12

3. Simplify the product:
y + 5 = (1/3)x − 4

4. Solve for the y-variable (subtract 5 from both sides):
y = (1/3)x − 9

(Check: at x = 12, y = 4 − 9 = −5, which matches the given point.)