To find the equation of line $v$, we follow these steps:

1. Identify the slope of line $u$:

The equation of line $u$ is given as: $y = 2x + \frac{8}{9}$ From this equation, we can see that the slope of line $u$ is $2$ (since the coefficient of $x$ is the slope).

2. Use the slope for line $v$:

Since line $v$ is parallel to line $u$, it will have the same slope. Therefore, the slope of line $v$ is also $2$.

3. Use the point (7, 9) to find the y-intercept:

The equation of line $v$ is in the form: $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept. We know that the slope $m = 2$, and we are given the point $(7, 9)$ on line $v$.

Substitute $x = 7$ and $y = 9$ into the equation to solve for $b$: $9 = 2(7) + b$ $9 = 14 + b$ $b = 9 - 14$ $b = -5$

4. Write the equation of line $v$:

Now that we know the slope $m = 2$ and the y-intercept $b = -5$, the equation of line $v$ is: $y = 2x - 5$

Final Answer:

The equation of line $v$ is: $y = 2x - 5$

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Would you like any further details or clarification on this process? Here are some related questions that might help you explore this topic:

1. How do you find the slope of a line from two points?
2. How do you determine the equation of a line when given two points?
3. What does it mean for two lines to be parallel?
4. How do you convert the equation of a line from standard form to slope-intercept form?
5. What is the difference between a slope of 0 and an undefined slope?

Tip: When solving for the y-intercept, always substitute the given point into the equation with the slope to isolate and find $b$.