On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 1) and (0, 1). everything to the left of the line is shaded. which linear inequality is represented by the graph? y > 2x + 2 y ≥ one-halfx + 1 y > 2x + 1 y ≥ one-halfx + 2

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  (c)  y > 2x + 1

Step-by-step explanation:

The line has a rise of 2 for a run of 1, so a slope of 2. Its y-intercept is 1, so the equation of the line is ...

  m = rise/run = 2/1 = 2; b = 1

  y = mx +b . . . . . . slope-intercept form

  y = 2x +1

The shading is above the line, and does not include the line, so the graph is of ...

  y > 2x +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.