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We are tasked with writing the equation of a line in slope-intercept form, given that it passes through the point \((-6, 7)\) and has a slope of \(\frac{3}{2}\).

### Slope-intercept form of a line:
The slope-intercept form is:
\[
y = mx + b
\]
where:
- \(m\) is the slope, and
- \(b\) is the y-intercept.

We know:
- \(m = \frac{3}{2}\),
- The line passes through the point \((-6, 7)\).

Now, we can substitute these values into the slope-intercept form to find \(b\) (the y-intercept).

1. Substitute the point \((-6, 7)\) into the equation \(y = mx + b\):
\[
7 = \frac{3}{2}(-6) + b
\]
2. Solve for \(b\):
\[
7 = -9 + b
\]
\[
b = 7 + 9 = 16
\]

### Final Equation:
Now that we have \(b = 16\), the equation of the line is:
\[
y = \frac{3}{2}x + 16
\]

Would you like a more detailed explanation, or do you have any questions?

Here are five related questions to expand on this concept:
1. How do we find the equation of a line when given two points?
2. How do we convert the slope-intercept form to standard form?
3. What is the geometric interpretation of the slope of a line?
4. How can we find the equation of a line perpendicular to this one?
5. What would the equation look like if the slope were negative?

**Tip:** Always substitute the coordinates of a known point into the slope-intercept equation to solve for the y-intercept efficiently!

A line passes through the point (-6, 7) and has a slope of 3/2. Write an equation in slope-intercept form for this line.

Learn how to find the equation of a line in slope-intercept form that passes through the point (-6, 7) with a slope of 3/2. This problem covers key algebraic concepts including linear equations, slope-intercept form, and conversion from point-slope to slope-intercept form. Suitable for students in Grades 7-9.

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