Write an equation for the line that passes through the points (-8,5) and (-2,9) in slope-intercept form.

y = x +

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m =

with (x₁, y₁ ) = (- 8, 5) and (x₂, y₂ ) = (- 2, 9)

m = = = , thus

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (- 2, 9 ), then

9 = - + c ⇒ c = 9 + =

y = x + ← equation of line

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.