Final answer:
The equation, in point-slope form, for a line that goes through (8, −4) and has a slope of −5/6 is y = -5/6x + 4/3.
Step-by-step explanation:
The equation, in point-slope form, for a line that goes through the point (8,-4) and has a slope of -5/6 can be found using the formula y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values into the formula, we have y - (-4) = -5/6(x - 8).
Simplifying the equation, we get y + 4 = -5/6x + 20/6, which can be further simplified to
y = -5/6x + 8/6 or
y = -5/6x + 4/3.