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.