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!