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Let's solve this step-by-step:

We are given the equation of line \( g \):
\[
y = \frac{1}{3}x - 1
\]
We need to find the equation of line \( h \), which is parallel to line \( g \) and passes through the point \( (10, 2) \).

### 1. Identify the slope of the line \( h \):
Since line \( h \) is parallel to line \( g \), it will have the same slope. The equation of line \( g \) is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope. Here, the slope \( m \) of line \( g \) is \( \frac{1}{3} \).

Thus, the slope of line \( h \) is also \( \frac{1}{3} \).

### 2. Use the point-slope form of the equation of a line:
The point-slope form of a line's equation is:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line. For line \( h \), we have:
- Slope \( m = \frac{1}{3} \),
- Point \( (x_1, y_1) = (10, 2) \).

Substituting these values into the point-slope form:
\[
y - 2 = \frac{1}{3}(x - 10)
\]

### 3. Simplify to slope-intercept form:
Now, let's simplify this to get the equation in slope-intercept form:
\[
y - 2 = \frac{1}{3}x - \frac{10}{3}
\]
Add 2 to both sides to solve for \( y \):
\[
y = \frac{1}{3}x - \frac{10}{3} + 2
\]
Convert 2 to a fraction with the same denominator:
\[
y = \frac{1}{3}x - \frac{10}{3} + \frac{6}{3}
\]
Now, combine the constants:
\[
y = \frac{1}{3}x - \frac{4}{3}
\]

Thus, the equation of line \( h \) is:
\[
y = \frac{1}{3}x - \frac{4}{3}
\]

Would you like further clarification on any step, or do you have additional questions?

Here are 5 related questions to expand your understanding:
1. How do you find the equation of a line that is perpendicular instead of parallel?
2. What happens to the slope when two lines are perpendicular?
3. How can you determine the equation of a line given two points?
4. Can you find the x- and y-intercepts of line \( h \)?
5. How would the equation change if line \( h \) passed through a different point?

**Tip:** Always simplify fractions when combining constants, and make sure to adjust the denominator to match when adding or subtracting fractions.

Line g has an equation of y = (1/3)x - 1. Parallel to line g is line h, which passes through the point (10, 2). What is the equation of line h?

Learn how to find the equation of a line parallel to y = (1/3)x - 1 that passes through the point (10, 2). This problem covers important concepts such as slope-intercept form and point-slope form. Suitable for students in Grades 8-10.

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