Final answer:
To write the equation of a line that passes through point (8, -6) with a slope of -3/4 in slope-intercept form, substitute the slope and the point into the formula, solve for the y-intercept, and write the final equation as y = (-3/4)x - 3.
Step-by-step explanation:
To write an equation in slope-intercept form for a line that passes through the point (8, -6) and has a slope of -3/4, you can use the equation of a line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
First, substitute the slope (-3/4) into the equation: y = (-3/4)x + b. Next, to find the y-intercept (b), plug in the coordinates of the given point into this equation: (-6) = (-3/4)(8) + b. Solve for b to get: b = -6 - (-3/4)(8).
After calculation, b equals -3. Therefore, the equation of the line in slope-intercept form is y = (-3/4)x - 3.