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We are given a point \((-9, -8)\) and a slope \( \frac{-2}{3} \). The goal is to write the equation of the line in slope-intercept form, which is:

\[
y = mx + b
\]

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

### Step 1: Use the point-slope form of a line
The point-slope form of a line is:

\[
y - y_1 = m(x - x_1)
\]

Here, \((x_1, y_1)\) is the given point \((-9, -8)\), and \(m = \frac{-2}{3}\). Substituting these values into the point-slope formula:

\[
y - (-8) = \frac{-2}{3}(x - (-9))
\]

Simplify:

\[
y + 8 = \frac{-2}{3}(x + 9)
\]

### Step 2: Simplify and solve for \(y\)
Distribute the slope on the right side:

\[
y + 8 = \frac{-2}{3}x - 6
\]

Now, subtract 8 from both sides to isolate \(y\):

\[
y = \frac{-2}{3}x - 6 - 8
\]

\[
y = \frac{-2}{3}x - 14
\]

### Final equation
The equation of the line in slope-intercept form is:

\[
y = \frac{-2}{3}x - 14
\]

Would you like more details or have any questions?

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Here are some related questions:
1. How do you find the equation of a line given two points?
2. What does the slope of a line represent geometrically?
3. How would you graph a line given its equation in slope-intercept form?
4. How do you convert from slope-intercept form to standard form?
5. Can the slope of a line be positive if the line is going downwards?

**Tip:** When working with slope-intercept form, remember that the slope \(m\) represents the rate of change, and the y-intercept \(b\) is where the line crosses the y-axis.

A line passes through the point (-9, -8) and has a slope of -2/3. 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 (-9, -8) with a slope of -2/3. This step-by-step solution covers essential algebraic concepts such as slope-intercept form and point-slope form.

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