To find the equation of a line in standard form, given that the line passes through the point (-4, 2) and has a slope of $\frac{9}{2}$, we can follow these steps:

1. Point-slope form: The point-slope form of the equation of a line is: $y - y_1 = m(x - x_1)$ where $m$ is the slope and $(x_1, y_1)$ is the point on the line.

   Plugging in $m = \frac{9}{2}$, $x_1 = -4$, and $y_1 = 2$: $y - 2 = \frac{9}{2}(x + 4)$

2. Simplify: $y - 2 = \frac{9}{2}(x + 4) = \frac{9}{2}x + \frac{9}{2} \times 4$ $y - 2 = \frac{9}{2}x + 18$

   Now, add 2 to both sides: $y = \frac{9}{2}x + 20$

3. Convert to standard form: Standard form is usually written as: $Ax + By = C$ To convert, first multiply everything by 2 to eliminate the fraction: $2y = 9x + 40$

   Rearrange the terms: $9x - 2y = -40$

So, the equation of the line in standard form is: $9x - 2y = -40$

Would you like a more detailed explanation of any step?

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Here are 5 related questions for further practice:

1. How would the equation change if the slope were $-\frac{9}{2}$?
2. What is the equation of a line parallel to this one but passing through a different point, say (3, -5)?
3. How do you find the y-intercept directly from the equation in standard form?
4. What would be the equation of a perpendicular line passing through (-4, 2)?
5. How does the standard form of an equation differ from the slope-intercept form?

Tip: Always clear fractions in linear equations by multiplying through by the denominator when converting to standard form.