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

Let’s complete the work step by step based on your problem where a line passes through the point (12, –5) with a slope of \( \frac{1}{3} \).

### 1. Substitute known values for \( m \), \( x_1 \), and \( y_1 \):

Given:
- Slope \( m = \frac{1}{3} \)
- Point \( (x_1, y_1) = (12, -5) \)

Using the point-slope form of the line equation, which is:
\[
y - y_1 = m(x - x_1)
\]

Substituting the known values:
\[
y - (-5) = \frac{1}{3}(x - 12)
\]
Which simplifies to:
\[
y + 5 = \frac{1}{3}(x - 12)
\]

### 2. Distribute the slope through the parentheses:

Now we distribute \( \frac{1}{3} \) on the right side:
\[
y + 5 = \frac{1}{3}x - \frac{1}{3} \cdot 12
\]

Calculating \( \frac{1}{3} \cdot 12 \):
\[
\frac{1}{3} \cdot 12 = 4
\]

Thus, the equation becomes:
\[
y + 5 = \frac{1}{3}x - 4
\]

### 3. Distribute the slope through the parentheses (again):

This step is not necessary, as we’ve already performed the distribution. So, we can proceed directly to the next step.

### 4. Solve for the y-variable:

Now, isolate \( y \):
\[
y = \frac{1}{3}x - 4 - 5
\]

Simplifying:
\[
y = \frac{1}{3}x - 9
\]

### Final Answer:

So, the equation of the line passing through the point (12, –5) with a slope of \( \frac{1}{3} \) is:
\[
y = \frac{1}{3}x - 9
\]