A coordinate grid with 2 lines. The first line passes through (negative 4, negative 3), (0, negative 3), and (4, negative 3). The second line passes through (0, negative 5) and (2, 4). The lines appear to intersect at about one-half, negative 3. Solve the system of equations algebraically. Verify your answer using the graph.

y = 4x – 5

y = –3

What is the solution to the system of equations?

((StartFraction one-fourth EndFraction, negative 3), –3)
((StartFraction one-half EndFraction, negative 3), –3)
(–3, (negative 3, StartFraction 2 over 3 EndFraction))

square root

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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.