H. goes through (-3, -2) and parallel to y = 5 x +5

 y = 5x + 13

Step-by-step explanation:

Parallel means it has the same slope.  

Given line y = 5x + 5  --> the slope is 5, so parallel slope is 5

Use the Point-Slope formula: y - y₁ = m(x - x₁)  such that

y + 2 = 5(x + 3)          input m and (x₁, y₁) into the Point-Slope formula

y + 2 = 5x + 15          distributed

     y = 5x + 13          subtracted 2 from both sides

step-by-step explanation: you take each of the numbers and divide by the amount then you take the range

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.