Write the equation of a line in​ slope-intercept form that passes through the point ​(-7​, -5​) and is parallel to the graph of the equation y=10x-5.

To find the equation of a line in slope-intercept form that passes through a given point and is parallel to another line, we will use the slope-intercept form:

\[
y = mx + b
\]

where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept.

### Step 1: Determine the slope of the parallel line

The given line is:

\[
y = 10x - 5
\]

The slope of this line is the coefficient of \( x \), which is \( 10 \). Since parallel lines have the same slope, the slope of the desired line will also be \( 10 \).

### Step 2: Use the point-slope form to find the equation

The point given is \( (-7, -5) \), and the slope \( m = 10 \). The point-slope form of a line is:

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

Substitute the given point \( (-7, -5) \) and the slope \( 10 \):

\[
y - (-5) = 10(x - (-7))
\]

Simplify the equation:

\[
y + 5 = 10(x + 7)
\]

### Step 3: Convert to slope-intercept form

Now, distribute and simplify:

\[
y + 5 = 10x + 70
\]

Subtract \( 5 \) from both sides to solve for \( y \):

\[
y = 10x + 65
\]

### Final Equation

The equation of the line in slope-intercept form that passes through the point \( (-7, -5) \) and is parallel to the line \( y = 10x - 5 \) is:

\[
\boxed{y = 10x + 65}
\]

Would you like more details on any step or have any questions?

Here are some related questions you might find interesting:
1. How do you find the equation of a line perpendicular to a given line?
2. What are the different forms of linear equations?
3. How do you find the distance between a point and a line?
4. What is the significance of the slope in the context of linear equations?
5. How can you determine if two lines are parallel or perpendicular by their equations?

**Tip:** When finding equations of lines, remember that parallel lines always share the same slope, while perpendicular lines have slopes that are negative reciprocals.

Learn how to find the equation of a line in slope-intercept form that passes through the point (-7, -5) and is parallel to the line y = 10x - 5. This step-by-step guide covers key concepts such as slope-intercept form and the properties of parallel lines. Suitable for students in Grades 8-10.

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