Question

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.

Answer 1

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

Explanation:

Answer 2

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

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
`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

- 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)

∵
`m_(1)=(4225-1990)/(5-2)=745`

∵
`m_(2)=(7205-4225)/(9-5)=745`

∵
`m_{3=(7205-1990)/(9-2)}=745`

∴ 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