Y=1/2x - 2 and y=-3x+5 solve this system by substitution

I. y = 1/2*x - 2

II . y = -3*x + 5

1/2*x - 2 = -3*x + 5

7/2*x - 2 = 5

7/2*x = 7

x = 7 * 2/7 = 2

y = 1/2*2 - 2 = -1

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.