Respuesta :
Answer:
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 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- 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)
∵ [tex]m_{1}=\frac{4225-1990}{5-2}=745[/tex]
∵ [tex]m_{2}=\frac{7205-4225}{9-5}=745[/tex]
∵ [tex]m_{3=\frac{7205-1990}{9-2}}=745[/tex]
∴ 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
Answer:
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:
