Final answer:
The equation of the linear function is f(x) = 0.6x + 1.8, derived by first calculating the slope using two given points and then using the point-slope form to find the equation.
Step-by-step explanation:
To find the equation of a linear function given that f(-3) = 0 and f(2) = 3, we will first calculate the slope (m) of the line using the slope formula: m = (y2 - y1) / (x2 - x1). In this case, (x1, y1) = (-3, 0) and (x2, y2) = (2, 3), so our slope is (3 - 0) / (2 - (-3)) = 3 / 5 = 0.6.
Now that we have the slope, we can use point-slope form to find the equation of the line, which is written as y - y1 = m(x - x1). Substituting our known point (-3, 0) and our calculated slope into the equation, we get y - 0 = 0.6(x - (-3)), which simplifies to y = 0.6(x + 3).
Expanding this we get y = 0.6x + 1.8, which is the equation for the linear function f(x).