Write the equation of the line that passes through the points s(−2,−2) and (8,0). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

To find the equation of the line passing through the points \( s(-2, -2) \) and \( (8, 0) \), we can use the point-slope form of the equation of a line, which is:

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

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

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

Substitute the given points \( (-2, -2) \) and \( (8, 0) \):

\[
m = \frac{0 - (-2)}{8 - (-2)} = \frac{0 + 2}{8 + 2} = \frac{2}{10} = \frac{1}{5}
\]

### Step 2: Use point-slope form
Now, substitute the slope \( m = \frac{1}{5} \) and one of the points, say \( (-2, -2) \), into the point-slope formula:

\[
y - (-2) = \frac{1}{5}(x - (-2))
\]

Simplifying:

\[
y + 2 = \frac{1}{5}(x + 2)
\]

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

Would you like more details or have any questions?

Here are 5 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. Can two different points ever have the same slope?
4. How would you find the midpoint between two points?
5. How can you determine if two lines are parallel?

**Tip:** Always double-check slope calculations when working with fractions to avoid small mistakes.

Learn how to find the equation of a line passing through the points (-2,-2) and (8,0) using the point-slope form. This detailed step-by-step solution explains how to calculate the slope and apply it to the point-slope equation. Suitable for students in Grades 8-10.

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