A line passes through the points (–7,0) and (7,–2).Write its equation in slope-intercept form.

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

### Step 1: Find the slope (m)
The slope \( m \) is given by the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \( (-7, 0) \) and \( (7, -2) \):
\[
m = \frac{-2 - 0}{7 - (-7)} = \frac{-2}{7 + 7} = \frac{-2}{14} = -\frac{1}{7}
\]
So, the slope \( m = -\frac{1}{7} \).

### Step 2: Find the y-intercept (b)
Now that we have the slope, we can use one of the points (I'll use \( (-7, 0) \)) to find the y-intercept \( b \). Plugging into the equation \( y = mx + b \):
\[
0 = -\frac{1}{7}(-7) + b
\]
Simplifying:
\[
0 = 1 + b \quad \Rightarrow \quad b = -1
\]

### Step 3: Write the equation of the line
Now that we know the slope \( m = -\frac{1}{7} \) and the y-intercept \( b = -1 \), the equation of the line in slope-intercept form is:
\[
y = -\frac{1}{7}x - 1
\]

Would you like more details or have any questions?

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Here are 5 related questions you might find useful:
1. How do you find the equation of a line given two points?
2. What is the relationship between the slope and the angle of a line?
3. How do you convert the equation of a line from slope-intercept form to standard form?
4. How does changing the slope affect the steepness of a line?
5. What is the significance of the y-intercept in real-world problems?

**Tip**: Always double-check your slope calculation, especially the signs, as they can change the direction of the line.

A line passes through the points (–7,0) and (7,–2). Write its equation in slope-intercept form.

Learn how to find the equation of a line that passes through the points (-7,0) and (7,-2) using the slope-intercept form. This problem covers key concepts such as calculating the slope and determining the y-intercept. Suitable for students in Grades 8-10.

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