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We are given that:

- The equation of line \( g \) is \( y = \frac{8}{9}x + 2 \).
- Line \( h \) is parallel to line \( g \) and passes through the point \( (9, 4) \).

Since line \( h \) is parallel to line \( g \), it has the same slope. The slope of line \( g \) is \( \frac{8}{9} \), so the slope of line \( h \) is also \( \frac{8}{9} \).

The equation of line \( h \) will be in the form of the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. We need to find \( b \), the y-intercept of line \( h \).

We know that line \( h \) passes through the point \( (9, 4) \), so we can substitute these values into the equation \( y = mx + b \):

\[
4 = \frac{8}{9}(9) + b
\]

Simplify the equation:

\[
4 = 8 + b
\]

Solving for \( b \):

\[
b = 4 - 8 = -4
\]

Thus, the equation of line \( h \) is:

\[
y = \frac{8}{9}x - 4
\]

Would you like more details on this, or do you have any questions?

Here are 5 related questions for practice:

1. What would be the equation of a line perpendicular to line \( g \)?
2. If line \( h \) passed through a different point, how would the equation change?
3. How do you determine if two lines are parallel or perpendicular just by looking at their equations?
4. What is the y-intercept of line \( g \), and how does it compare to that of line \( h \)?
5. How can you graph the equation of line \( h \) on a coordinate plane?

**Tip**: When two lines are parallel, their slopes are equal, but their y-intercepts can differ!

The equation of line g is y = (8/9)x + 2. Line h is parallel to line g and passes through (9, 4). What is the equation of line h?

Learn how to find the equation of a line parallel to another line with a detailed solution. In this example, the line h is parallel to line g and passes through the point (9, 4). The solution explains how to calculate the y-intercept and construct the equation of the line in slope-intercept form.

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