Final answer:
The equation for the line is y = -5/3x + 15 in slope-intercept form.
Step-by-step explanation:
The equation for the line that passes through the point (9, -14) and has a slope of -5/3 can be found using the point-slope form of a linear equation. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope. Substituting the values (9, -14) and -5/3 into the equation, we get:
y + 14 = -5/3(x - 9)
To convert this equation into slope-intercept form, we need to isolate y on one side of the equation. Simplifying the equation, we have:
y = -5/3x + 15
Therefore, the equation for the line is y = -5/3x + 15 in slope-intercept form.