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Let's solve the problem step by step:

We are given the equation for line \( k \):

\[
y + 5 = \frac{7}{5}(x - 10)
\]

First, we can rewrite it in slope-intercept form, \( y = mx + b \), where \( m \) is the slope.

1. Distribute \(\frac{7}{5}\) on the right-hand side:

\[
y + 5 = \frac{7}{5}x - \frac{7}{5} \cdot 10
\]

\[
y + 5 = \frac{7}{5}x - 14
\]

2. Subtract 5 from both sides to isolate \( y \):

\[
y = \frac{7}{5}x - 14 - 5
\]

\[
y = \frac{7}{5}x - 19
\]

So, the slope of line \( k \) is \( \frac{7}{5} \).

### Finding the equation of line \( l \)
Since line \( l \) is parallel to line \( k \), it has the same slope \( m = \frac{7}{5} \). The equation of line \( l \) passes through the point \((-3, -6)\).

Using the point-slope form of the line equation:

\[
y - y_1 = m(x - x_1)
\]

where \( (x_1, y_1) = (-3, -6) \) and \( m = \frac{7}{5} \), we can plug in the values:

\[
y - (-6) = \frac{7}{5}(x - (-3))
\]

\[
y + 6 = \frac{7}{5}(x + 3)
\]

Now distribute \( \frac{7}{5} \):

\[
y + 6 = \frac{7}{5}x + \frac{7}{5} \cdot 3
\]

\[
y + 6 = \frac{7}{5}x + \frac{21}{5}
\]

Subtract 6 from both sides to isolate \( y \):

\[
y = \frac{7}{5}x + \frac{21}{5} - 6
\]

Convert 6 to a fraction with a denominator of 5:

\[
y = \frac{7}{5}x + \frac{21}{5} - \frac{30}{5}
\]

Simplify:

\[
y = \frac{7}{5}x - \frac{9}{5}
\]

### Final Equation:
The equation of line \( l \) in slope-intercept form is:

\[
y = \frac{7}{5}x - \frac{9}{5}
\]

Let me know if you want further details or have any questions!

Here are 5 related questions:
1. How do you determine the slope of a line from its equation?
2. What is the point-slope form of a line, and when do you use it?
3. How do you know two lines are parallel?
4. How can you convert a point-slope equation to slope-intercept form?
5. How does changing the slope of a line affect its direction?

**Tip**: Always check if two lines are parallel by comparing their slopes!

The equation for line k can be written as y + 5 = (7/5)(x - 10). Line l is parallel to line k and passes through (-3, -6). What is the equation of line l?

Learn how to find the equation of a line parallel to y + 5 = (7/5)(x - 10) that passes through (-3, -6). This problem covers linear equations, parallel lines, and uses slope-intercept and point-slope forms. Ideal for students in Grades 8-10.

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