To find the equation of the line in standard form, we need to follow these steps:

Step 1: Find the slope ($m$) of the line

The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the points $(-4, 9)$ and $(2, -9)$: $m = \frac{-9 - 9}{2 - (-4)} = \frac{-18}{6} = -3$

Step 2: Use the point-slope form of a line

The point-slope form is: $y - y_1 = m(x - x_1)$ Using the slope $m = -3$ and the point $(-4, 9)$: $y - 9 = -3(x + 4)$

Step 3: Simplify to slope-intercept form

Expand and simplify: $y - 9 = -3x - 12$ $y = -3x - 3$

Step 4: Convert to standard form

The standard form of a line is: $Ax + By = C$ Rewriting $y = -3x - 3$ in standard form: $3x + y = -3$

Final Answer:

The equation of the line in standard form is: $\boxed{3x + y = -3}$

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Related Questions:

1. How do you find the equation of a line given a slope and a point?
2. What are the differences between standard form, slope-intercept form, and point-slope form?
3. How do you verify that a line passes through two given points?
4. Can a vertical line be written in standard form? How?
5. What is the process to convert a line from slope-intercept form to standard form?

Tip:

Always ensure that the coefficients $A$, $B$, and $C$ in the standard form are integers, and $A$ is positive.