Final answer:
To write the equation of a line in slope-intercept form that passes through the point (3, 9) with a slope of -5, use the equation y = mx + b. Plug in the slope and point to get y = -5x + 24 as the final equation.
Step-by-step explanation:
The student's question is about writing an equation in slope-intercept form. To write the equation of a line that passes through the point (3, 9) and has a slope of -5, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope (m = -5) and a point on the line (3, 9), we can substitute these values into the slope-intercept form to find the y-intercept:
y - 9 = -5(x - 3).
Simplifying this equation, we get:
y - 9 = -5x + 15
Adding 9 to both sides:
y = -5x + 24.
Therefore, the equation of the line in slope-intercept form is y = -5x + 24.