https://file.aiquickdraw.com/mathbot/file/17264422414905l9jgai6.jpg

To write the equation in slope-intercept form, we need to use the given point and slope. The slope-intercept form of a line is:

\[
y = mx + b
\]

where:
- \(m\) is the slope,
- \(b\) is the y-intercept.

From the problem:
- The slope \(m = \frac{3}{2}\),
- The point is \( (6, -9) \), which we can substitute into the equation to solve for \(b\) (the y-intercept).

Let's substitute the point into the equation and solve for \(b\):

\[
-9 = \frac{3}{2}(6) + b
\]

Simplifying:

\[
-9 = 9 + b
\]

Now solve for \(b\):

\[
b = -9 - 9 = -18
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = \frac{3}{2}x - 18
\]

This is the equation you can enter in the form.

Would you like more details or have any questions? Here are some related questions for practice:

1. How do you find the slope if two points are given instead of one point and slope?
2. What does the slope represent in a real-world context?
3. How can you convert from slope-intercept form to standard form?
4. How do parallel and perpendicular slopes compare?
5. What happens to the graph of a line if you change the value of the slope?

**Tip:** When working with slope-intercept form, remember that the slope determines how steep the line is, while the intercept shows where the line crosses the y-axis.

A line passes through the point (6, -9) and has a slope of 3/2. Write an equation in slope-intercept form for this line.

Learn how to write the equation of a line in slope-intercept form using the point (6, -9) and the slope 3/2. This solution covers how to find the y-intercept by substituting the point into the slope-intercept equation.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation