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The problem asks to write the equation of a line in the standard form \( Ax + By = C \), given the slope \( \frac{2}{3} \) and that the line passes through the point \( (9, -5) \).

We can use the point-slope form of a line to start, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line.

### Step 1: Plug in the values.
Given:
- \( m = \frac{2}{3} \)
- \( (x_1, y_1) = (9, -5) \)

The point-slope form becomes:
\[
y + 5 = \frac{2}{3}(x - 9)
\]

### Step 2: Simplify the equation.
First, distribute the \( \frac{2}{3} \) on the right side:
\[
y + 5 = \frac{2}{3}x - 6
\]

Next, subtract 5 from both sides:
\[
y = \frac{2}{3}x - 11
\]

### Step 3: Convert to standard form \( Ax + By = C \).
Multiply both sides of the equation by 3 to eliminate the fraction:
\[
3y = 2x - 33
\]

Now move \( 2x \) to the left side:
\[
-2x + 3y = -33
\]

### Step 4: Multiply by -1 (optional, to make \( A \) positive).
\[
2x - 3y = 33
\]

Thus, the equation of the line in standard form is:
\[
2x - 3y = 33
\]

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you derive the equation of a line if you are given two points instead of one point and the slope?
2. Why is the slope-intercept form of a line useful for graphing?
3. Can you derive the slope formula from two points on a line?
4. How do you recognize a line in standard form from its graph?
5. What are the differences between the general form and standard form of a line's equation?

**Tip:** When converting equations into standard form, make sure all coefficients are integers, and typically, the coefficient of \( x \) (i.e., \( A \)) is positive.

A line passes through point (9, -5) and has a slope of 2/3. Write an equation in Ax + By = C form for this line. Use integers for A, B, and C.

Learn how to write the equation of a line in standard form that passes through the point (9, -5) with a slope of 2/3. This problem involves key algebraic concepts, including point-slope form and the conversion to standard form. Suitable for students in Grades 8-10.

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