What is an equation of the line that passes through the points (-6,-4) and
(-4,0)?

y = 2x + 8

Step-by-step explanation:

the equation of a line in slope-intercept form is.

y = mx+b

where m is the slope and b the y-intercept

to calculate m use the gradient formula

m = (y2−y1 ) / (x2−x1)

let (x1,y1)=(-6,-4) and (x2,y2)=(-4,0)

m = (0 - (-4)) / (-4 - (-6) = 2

y = 2x+b←is the partial equation

to find b substitute either of the 2 given points

into the partial equation

using (-6, -4) then

-4 = -12+b⇒b=8

y = 2x + 8←is the 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.