Final answer:
To write the equation of a linear function in point-slope form with m=3 and f(2) = -9, use the formula y - y1 = m(x - x1) with the point (2, -9), resulting in y + 9 = 3(x - 2).
Step-by-step explanation:
The question asks us to write the equation of a linear function in point-slope form given the slope (m) is 3 and the function value at x = 2 (f(2)) is -9. The point-slope form of a line's equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Since we know that f(2) = -9, we have a point (2, -9). Substituting the given values into the point-slope form equation, we get y - (-9) = 3(x - 2), which simplifies to y + 9 = 3(x - 2).
The equation of the linear function in point-slope form is y - y1 = m(x - x1). Since it is given that m = 3 and f(2) = -9, we have the point (2, -9). Substituting these values into the point-slope form, we get:
y - (-9) = 3(x - 2)
y + 9 = 3x - 6
y = 3x - 6 - 9
y = 3x - 15