Hello, Ahmed,
Given that we have a straight line, we'll look for an equation of the form y = mx + b, where m is the slope and b the y=intercept.
The f(-4) = 5, and f(3) = 0 mean that for the value of (x), we get the corresponding vale of y. So we have two points we know are on the line.
(-4, 5) and (3, 0)
We can find m, the slope, by looking at what's known as the Rise/Run. The rise is the change in y as x is changed. In this case we start at x = -4 and move to x = 3. That is a "run" of (3 - (-4)), or 7. The change in y over this interval is (0 -5), or -5 (the rise). The .slope is the rise/run, or (-5/7) = -(5/7).
y = -(5/7)x + b
To find b, use one of the two points in the equation and solve for b.
y = -(5/7)x + b
0 = -(5/7)*(3) + b
b = (15/7)
y = -(5/7)x + (15/7)
The slope is negative since y gets smaller as x increases. The line crosses the y axis at (15/7). That point is (0,15/7)
Bob
