Question: Write the equation of the line through the indicated point with the indicated slope. Write the final answer in the form $y = mx + b$.\nm = -9; (5, -2)\nThe equation of the line is __.\n(Type your answer in slope-intercept form.)
1. **State the problem:** We need to find the equation of a line with slope $m = -9$ passing through the point $(5, -2)$ in slope-intercept form $y = mx + b$.
2. **Recall the formula:** The slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept.
3. **Use the point-slope form to find $b$:** Substitute $m = -9$, $x = 5$, and $y = -2$ into the equation:
$$-2 = -9(5) + b$$
4. **Simplify and solve for $b$:**
$$-2 = -45 + b$$
Add $45$ to both sides:
$$-2 + 45 = b$$
$$43 = b$$
5. **Write the final equation:** Substitute $m$ and $b$ back into slope-intercept form:
$$y = -9x + 43$$
**Answer:** The equation of the line is $y = -9x + 43$.