Write the slope-intercept form of the line that has a slope of 2 and intersects the line, 2x - 3y = 6 at x = 3

so these two lines intersect at x = 3 hmmmm what's the y-coordinate of the second line at that point?

so the y-coordinate of that second line is 0, so the point there is (3, 0) then.

so the first line is, a line that has a slope of 2 and passes through (3, 0).

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.