Final answer:
To find the equation of a line in slope-intercept form given two points, calculate the slope using the two points, and then use one point to find the y-intercept. The derived equation is y = -1/4x + 19/4.
Step-by-step explanation:
To write an equation in slope-intercept form, which is y = mx + b, we need to find the slope (m) and the y-intercept (b). Given that f(-1) = 5 and f(3) = 4, we can interpret these as points on the graph: (-1, 5) and (3, 4). To find the slope, we use the formula m = (y2 - y1) / (x2 - x1).
The slope calculation would be as follows:
m = (4 - 5) / (3 - (-1)) = -1 / 4.
Now that we have the slope, we need to find the y-intercept. We can use one of the points and the slope to solve for b in the equation y = mx + b. Let's use point (3, 4).
The setup is:
4 = (-1/4)(3) + b
4 = -3/4 + b
4 + 3/4 = b
b = 4.75 or b = 19/4
So the equation of the line is y = -1/4x + 19/4.