To solve the problem of writing an equation in point-slope form for the line passing through the point $(-9, 7)$ with slope $m = 3$, we use the point-slope formula:

$y - y_1 = m(x - x_1),$

where $(x_1, y_1)$ is the given point and $m$ is the slope.

Substituting the values:

$y - 7 = 3(x - (-9)),$

Simplify the equation: $y - 7 = 3(x + 9).$

Final Equation in Point-Slope Form:

$y - 7 = 3(x + 9).$

Would you like further clarification or a step-by-step explanation?

Here are some related questions to explore further:

1. How do you convert the point-slope form to slope-intercept form?
2. What is the general form of a linear equation, and how is it related to point-slope form?
3. If the slope is negative, how does it affect the graph of the line?
4. Can you use a different point on the same line to derive the same equation?
5. How can you graph the line given the point-slope form?

Tip: Always double-check whether the slope and point are substituted correctly to avoid small errors in calculations.