https://file.aiquickdraw.com/mathbot/file/1730513762684kuyhcvux.jpg

To find the equation of a line that is perpendicular to the line graphed in the image, we first need to determine the slope of the original line.

### Step 1: Determine the Slope of the Original Line
1. The line in the graph passes through two points:
   - Point A: \((-7, 6)\)
   - Point B: \((0, -2)\)

2. We can calculate the slope \( m \) of this line using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   where \((x_1, y_1) = (-7, 6)\) and \((x_2, y_2) = (0, -2)\).

3. Substituting the values:
   \[
   m = \frac{-2 - 6}{0 - (-7)} = \frac{-8}{7}
   \]
   So, the slope of the given line is \( -\frac{8}{7} \).

### Step 2: Find the Slope of the Perpendicular Line
To be perpendicular, a line’s slope must be the negative reciprocal of the original slope. The negative reciprocal of \( -\frac{8}{7} \) is \( \frac{7}{8} \).

### Step 3: Write the Equation of the Perpendicular Line
The equation of a line can be written in the form:
\[
y = mx + b
\]
where \( m \) is the slope of the line.

Since the slope of the perpendicular line is \( \frac{7}{8} \), the equation of any line perpendicular to the original line will have the form:
\[
y = \frac{7}{8}x + b
\]
where \( b \) is the y-intercept, which can vary.

Therefore, **an equation of a line that is perpendicular to the line graphed** could be:
\[
y = \frac{7}{8}x + b
\]
where \( b \) can be any constant.

Would you like further details on finding the y-intercept for specific points, or do you have any other questions?

### Related Questions
1. How do you calculate the slope between two points on a line?
2. What does it mean for two lines to be perpendicular in terms of their slopes?
3. How do you write the equation of a line given a point and a slope?
4. Can there be multiple perpendicular lines to a given line? Why or why not?
5. How does the concept of slope relate to the steepness of a line?

### Tip:
Remember, perpendicular lines have slopes that are negative reciprocals of each other.

Which is an equation of a line that is perpendicular to the line graphed below?

Learn how to find the equation of a line perpendicular to a given line on a graph. This guide covers calculating slopes, identifying perpendicular relationships, and writing the equation of the perpendicular line. Suitable for Grades 8-10.

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