Let's break down the problem from the image step by step.

We are given:

1. The slope of the line, $m = \frac{2}{7}$.
2. A point on the line, $(-9, 6)$.
3. We need to find the $y$-coordinate of another point, $(5, y)$.

We can use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Where:

• $m = \frac{2}{7}$ (the slope),
• $(x_1, y_1) = (-9, 6)$ (the given point),
• $(x, y) = (5, y)$ (the point we're trying to find the $y$-coordinate for).

Substitute these values into the equation:

$y - 6 = \frac{2}{7}(x - (-9))$ $y - 6 = \frac{2}{7}(x + 9)$

Now, substitute $x = 5$ into this equation:

$y - 6 = \frac{2}{7}(5 + 9)$ $y - 6 = \frac{2}{7}(14)$ $y - 6 = 2 \times 2$ $y - 6 = 4$ $y = 4 + 6 = 10$

Therefore, the missing $y$-coordinate is $10$. The point is $(5, 10)$.

Would you like more details on this process, or do you have any questions? Here are some related questions:

1. How do you convert the slope-intercept form to point-slope form?
2. What does the slope of a line represent in real-world situations?
3. Can you find the equation of the line passing through the points $(-9, 6)$ and $(5, 10)$?
4. How do you find the midpoint between two points on a line?
5. What happens to the slope of a line when the coordinates of the points change direction?

Tip: Always substitute carefully in slope-related problems to avoid errors with signs!