Me, i'm a little confused on this one.

the graph shows the solution to which system of equations?

a)
y = x + 2 and y = -x - 4

b)
y = 3x + 7 and y = x + 12

c)
y = 2x - 3 and y = −2x + 1

d)
y = -x + 4 and y = −2x + 5

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.