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!