Question

The graph shows the amount of money in a students bank at the end of each week. If the pattern continues how much in dollars will be in the bank at the end of week 11. Round to nearest whole number

Answer 1

At the end of week 11, there will be $130

Step-by-step explanation:

To determine the amount in the 11th week, we need to find the equation relating the amount in the bank with the number of weeks.

We will use the equation of line:

y = mx + b

m = slope, b = y-intercept

To get the slope will [pick any two points on the graph

Using points (1, 30) and (3, 50)

`\begin{gathered} s\text{lope = }\frac{50\text{ - 30}}{3-1} \\ \text{slope = 20/2 = 10} \end{gathered}`

Next, we will find the y-intercept. The point where the line crosses the y axis is the y-intercept

In our graph we only have dots. If we are to draw a straight line, the line will cross the y axis at y = 20

So y-intercept = b = 20

To confirm our value for b, we can use any of the point and slope

Using (1, 30) = (x, y), m = 10

y = mx + b

30 = 10(1) + b

30 = 10 + b

b = 30 - 10 = 20 (correct)

substitute for m and b in the equation:

y = 10x + 20

For week 11, the value of x = 11

y = 10(11) + 20

y = 110 + 20

y = 130

At the end of week 11, there will be $130