Write the equation of the line that passes through the points (−9,−9) and (−8,1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line that passes through the points \((-9, -9)\) and \((-8, 1)\), we follow these steps:

### 1. Find the slope \( m \)
The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the given points \((-9, -9)\) and \((-8, 1)\):

\[
m = \frac{1 - (-9)}{-8 - (-9)} = \frac{1 + 9}{-8 + 9} = \frac{10}{1} = 10
\]

### 2. Use the point-slope form
The point-slope form of a line is:

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

Using the point \((-9, -9)\) and the slope \(m = 10\), we substitute these values into the formula:

\[
y - (-9) = 10(x - (-9))
\]

Simplify the equation:

\[
y + 9 = 10(x + 9)
\]

This is the equation of the line in point-slope form.

Would you like more details or have any questions?

Here are some related questions:
1. How do you convert point-slope form to slope-intercept form?
2. What is the equation of a vertical line passing through two points?
3. How do you find the slope if one of the points is at the origin?
4. What are the intercepts of the line given by this equation?
5. How do you graph a line using the point-slope form?

**Tip:** Always check the slope calculation first, as it determines the steepness and direction of the line.

Learn how to write the equation of a line passing through the points (-9, -9) and (-8, 1) using point-slope form. This step-by-step guide covers key concepts in coordinate geometry and linear equations, suitable for students in Grades 8-10.

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