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We are tasked with finding the equation of a line that passes through the point \((-6, -8)\) and has a slope of \(\frac{3}{2}\). We need to write the equation in the form \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers.

### Step 1: Use the point-slope form of the equation of a line
The point-slope form is given by:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is a point on the line, and \(m\) is the slope. Plugging in the point \((-6, -8)\) and the slope \(m = \frac{3}{2}\), we get:
\[
y - (-8) = \frac{3}{2}(x - (-6))
\]
Simplify the equation:
\[
y + 8 = \frac{3}{2}(x + 6)
\]

### Step 2: Eliminate the fraction
To eliminate the fraction, multiply both sides of the equation by 2:
\[
2(y + 8) = 3(x + 6)
\]
Simplify:
\[
2y + 16 = 3x + 18
\]

### Step 3: Rearrange to \(Ax + By = C\) form
Move all terms involving \(x\) and \(y\) to one side of the equation:
\[
3x - 2y = -2
\]

Thus, the equation in standard form is:
\[
3x - 2y = -2
\]
where \(A = 3\), \(B = -2\), and \(C = -2\).

Would you like more details or have any questions? Here are 5 related questions to deepen your understanding:

1. How would you graph the line \(3x - 2y = -2\)?
2. How does the slope \(\frac{3}{2}\) affect the steepness of the line?
3. What is the significance of the point \((-6, -8)\) in the equation?
4. How would the equation change if the slope were negative?
5. How do you convert from point-slope form to standard form for any equation?

**Tip:** When converting from point-slope to standard form, always clear fractions by multiplying through by the denominator first.

A line passes through point (-6, -8) and has a slope of 3/2. Write an equation in Ax + By = C form for this line. Use integers for A, B, and C.

Learn how to find the equation of a line that passes through the point (-6, -8) with a slope of 3/2. This step-by-step solution converts the point-slope form to the standard form Ax + By = C. Ideal for students in Grades 9-12 studying algebra and linear equations.

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