A line passes through the points (–8,9) and (–2,–9). Write its equation in slope-intercept form.

To write the equation of a line in slope-intercept form, \( y = mx + b \), we first need to find the slope \( m \) and then determine the \( y \)-intercept \( b \).

### Step 1: Calculate the slope (\( m \))

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

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

Given the points \( (-8, 9) \) and \( (-2, -9) \), let's plug them into the formula:

\[
m = \frac{-9 - 9}{-2 - (-8)} = \frac{-18}{-2 + 8} = \frac{-18}{6} = -3
\]

So, the slope \( m = -3 \).

### Step 2: Find the \( y \)-intercept (\( b \))

Now that we know the slope is \( -3 \), we use one of the points to find the \( y \)-intercept. We'll use the point \( (-8, 9) \). Substituting into the equation \( y = mx + b \):

\[
9 = -3(-8) + b
\]

Simplify:

\[
9 = 24 + b
\]

Solve for \( b \):

\[
b = 9 - 24 = -15
\]

### Step 3: Write the equation

Now that we have the slope \( m = -3 \) and the intercept \( b = -15 \), the equation of the line is:

\[
y = -3x - 15
\]

Would you like further explanation or have any questions?

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Here are 5 related questions for practice:
1. What is the equation of a line that passes through \( (1, 2) \) and \( (4, 5) \)?
2. How do you find the slope between two points if both points have the same \( y \)-coordinate?
3. Can you rewrite the equation \( y = -3x - 15 \) in standard form?
4. What happens to the slope if the two points have the same \( x \)-coordinate?
5. How would you find the equation of a line parallel to \( y = -3x - 15 \) that passes through \( (0, 5) \)?

**Tip:** The slope of a line measures its steepness; a negative slope means the line goes down as you move to the right.

A line passes through the points (–8,9) and (–2,–9). Write its equation in slope-intercept form.

Learn how to find the equation of a line in slope-intercept form that passes through the points (-8,9) and (-2,-9). This problem involves calculating the slope and determining the y-intercept using key algebraic concepts. Suitable for students in Grades 8-10.

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