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The problem shown in the image asks to find the equation of a line in standard form that passes through the point (-4, 2) and has a slope of \( \frac{9}{2} \).

### Solution Outline:

1. **Use Point-Slope Form**:  
   The point-slope form of a line equation is:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through.

   Plug in \( m = \frac{9}{2} \) and the point \( (-4, 2) \):
   \[
   y - 2 = \frac{9}{2}(x + 4)
   \]

2. **Simplify the Equation**:
   \[
   y - 2 = \frac{9}{2}(x + 4)
   \]
   Multiply out:
   \[
   y - 2 = \frac{9}{2}x + 18
   \]
   Add 2 to both sides:
   \[
   y = \frac{9}{2}x + 20
   \]

3. **Convert to Standard Form**:  
   To get the equation in standard form \( Ax + By = C \), clear the fraction by multiplying through by 2:
   \[
   2y = 9x + 40
   \]
   Rearrange to get all terms on one side:
   \[
   9x - 2y = -40
   \]

4. **Compare to Answer Choices**:  
   The equation in standard form is \( 9x - 2y = -40 \), which matches choice **C**.

Thus, the correct answer is **C**.

### Do you have any questions, or would you like more details?  
Here are 5 related questions:
1. How do you convert point-slope form to slope-intercept form?
2. How do you find the equation of a line given two points?
3. What is the general form of a linear equation?
4. How do you interpret the slope and y-intercept of a linear equation?
5. How do you verify if a point lies on a line given its equation?

**Tip**: Always double-check the sign of each term when converting between forms of linear equations!

Which equation in standard form has a graph that passes through the point (-4, 2) and has a slope of 9/2?

Learn how to find the equation of a line in standard form that passes through the point (-4, 2) with a slope of 9/2. This step-by-step solution converts from point-slope form to standard form. Suitable for Grades 9-10.

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