To solve for the equation of line $g$, we need to keep in mind two key points:

1. Parallel lines have the same slope. The slope of line $f$ is given as $-\frac{1}{10}$, so line $g$ must have the same slope.
2. The point $(10, -2)$ lies on line $g$, so we will use the point-slope form to find the equation of line $g$.

Step 1: Use the point-slope form

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is a point on the line.

We already know:

• $m = -\frac{1}{10}$ (since line $g$ is parallel to line $f$),
• $(x_1, y_1) = (10, -2)$.

Substitute these values into the point-slope form: $y - (-2) = -\frac{1}{10}(x - 10)$ $y + 2 = -\frac{1}{10}(x - 10)$

Step 2: Simplify the equation

Distribute the slope on the right-hand side: $y + 2 = -\frac{1}{10}x + 1$ Subtract 2 from both sides: $y = -\frac{1}{10}x + 1 - 2$ $y = -\frac{1}{10}x - 1$

Step 3: Identify the correct option

The equation of line $g$ is $y = -\frac{1}{10}x - 1$, which corresponds to the second option:

$\boxed{y = -\frac{1}{10}x - 1}$

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Here are 5 related questions:

1. How do we find the slope of a line given two points?
2. What are the properties of parallel lines in terms of slope?
3. How do you convert point-slope form to slope-intercept form?
4. Can two lines have the same slope and not be parallel?
5. How can you find the equation of a line perpendicular to another line?

Tip: Parallel lines always share the same slope but have different y-intercepts unless they are identical.