To solve for the equation of the line passing through the point \((9, -4)\) with a slope of \(-2/3\), we can use the point-slope form of a linear equation:

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

Where:
- \((x_1, y_1)\) is the point on the line, in this case, \((9, -4)\),
- \(m\) is the slope, given as \(-2/3\).

Substituting the values into the equation:

\[
y - (-4) = \frac{-2}{3}(x - 9)
\]

Simplifying this:

\[
y + 4 = \frac{-2}{3}(x - 9)
\]

To further simplify:

\[
y + 4 = \frac{-2}{3}x + \frac{-2}{3} \times (-9)
\]

\[
y + 4 = \frac{-2}{3}x + 6
\]

Finally, subtract 4 from both sides to solve for \(y\):

\[
y = \frac{-2}{3}x + 6 - 4
\]

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

Thus, the equation of the line is:

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

Would you like further details or have any questions?

Here are five related questions:
1. How do you convert from point-slope form to slope-intercept form?
2. What is the significance of the slope in a linear equation?
3. How would the equation change if the slope were positive instead of negative?
4. How can you find the x-intercept of this line?
5. What is the difference between point-slope form and standard form of a line equation?

**Tip:** Remember, the slope indicates how steep a line is and in which direction it tilts. A negative slope means the line goes downwards from left to right.

Learn how to determine the equation of a line that passes through the point (9, -4) with a slope of -2/3 using the point-slope form and simplifying to slope-intercept form. Ideal for students in Grades 8-10.

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