The equation of line $j$ is given as:

$y = -\frac{5}{7}x - 10$

Since line $k$ is parallel to line $j$, it will have the same slope. The slope of line $j$ is $-\frac{5}{7}$, so the slope of line $k$ is also $-\frac{5}{7}$.

Now, we use the point-slope form of a line equation to find the equation of line $k$. The point-slope form 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 $k$, $m = -\frac{5}{7}$ and the given point is $(-9, 5)$.

Substitute the values:

$y - 5 = -\frac{5}{7}(x + 9)$

Now, distribute the slope on the right-hand side:

$y - 5 = -\frac{5}{7}x - \frac{5}{7} \times 9$

$y - 5 = -\frac{5}{7}x - \frac{45}{7}$

Next, add 5 to both sides:

$y = -\frac{5}{7}x - \frac{45}{7} + 5$

Convert 5 to a fraction with denominator 7:

$5 = \frac{35}{7}$

Now add the fractions:

$y = -\frac{5}{7}x - \frac{45}{7} + \frac{35}{7}$

$y = -\frac{5}{7}x - \frac{10}{7}$

Thus, the equation of line $k$ in slope-intercept form is:

$y = -\frac{5}{7}x - \frac{10}{7}$

Would you like a more detailed explanation of the steps?

Related Questions:

1. How do you find the slope of a line from two points?
2. What is the relationship between parallel lines and their slopes?
3. How can you convert a point-slope equation into slope-intercept form?
4. What is the general form of a linear equation, and how does it differ from slope-intercept form?
5. How do you find the equation of a line perpendicular to a given line?

Tip: For parallel lines, always ensure their slopes are identical.