Answer:
The answer is -5/2
Explanation:
The graph of the linear function f(x) passes through the points (-2, 4) and (2, -4) and has a negative slope.
To find the value of x for which f(x) = 5, we need to find the equation of the line first.
The slope of the line can be calculated as follows:
slope = (y2 - y1) / (x2 - x1) = (-4 - 4) / (2 - (-2)) = -8 / 4 = -2
Using the point-slope form of the equation of a line, we can write:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is any point on the line. Let’s use the point (-2, 4):
y - 4 = -2(x - (-2)) y - 4 = -2(x + 2) y - 4 = -2x - 4 y = -2x
Now we can substitute y = 5 and solve for x:
5 = -2x x = -5/2
So, the value of x for which f(x) = 5 is -5/2.