In a graph, x represents the number of months since a
business opened, and y represents the total amount of
money the business has earned. the following three
points are from the graph:
(2, 1990) (5, 4225) (9, 7205)
find the slope and y-intercept. explain what each
represents.

The slope is 745 and the y-intercept is 500

The slope means The amount of money increases by $745 per month

The y-intercept means the business opened with initial amount $500

Step-by-step explanation:

* Lets explain how to solve the question

- The graph represents the relation between the number of months

  since the business opened and the total amount of money the

  business has earned

- The x-axis represents the number of month

- The y-axis represents the amount of money

- In the line the slopes from any two points on the line are equal

- The slope of the line whose end-points are (x1 , y1) and (x2 , y2)

  is

- The equation of the line is y = mx + c ,where m is the slope of the line

 and c is the y-intercept

* Lets check is the relation between x and y is linear by calculating the

 slopes between each to points

∵ (2 , 1990) , (5 , 4225) , (9 , 7205) are points from the graph

- m1 is the slope of the points (2 , 1990) and (5 , 4225) , m2 is the slope

 of the points (5 , 42250) and (9 , 7205) , m3 is the slope of the points

 (2 , 1990) and (9 , 7205)

∵

∵

∵

∴ m1 = m2 = m3 = 745

∴ The relation between the number of months and the amount of

   money is linear

* The slope is 745

∵ The form of the linear equation is y = mx + c

∵ m = 745

∴ y = 745 x + c

- The y-intercept means the line intersect the y-axis at point (0 , c),

  then to find c substitute x and y of the equation by the coordinates

  of any point on the line

∵ x = 2 , y = 1990

∴ 1990 = 745(2) + c

∴ 1990 = 1490 + c ⇒ subtract 1490 from both sides

∴ c = 500

∵ c is the y-intercept

* The y-intercept is 500

* The slope represents the rate of increasing of money per month

∴ The amount of money increases by $745 per month

* The y-intercept represents the initial amount of money when the

  business opened

∴ The business opened with initial amount $500

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.

according to egenuity the answer is

step-by-step explanation:

d. 344.22