Question

each saturday, tina mows lawns to earn extra money which she puts into a savings account. the graph shows the balance of tina’s savings accounts over the first six weeks of mowing lawns. according to this pattern, how much will tina have in her account after 15 weeks of mowing lawns?

Answer 1

$255

Explanation:

First, we need to generate an equation in slope-intercept form, y = mx + b, that represents the graph. To do this, we need to find b = initial value (y-intercept) and m = slope (money she puts in her account each week).

x = number of weeks

y = balance ($)

✔️Slope (m) = change in y/change in x

Using two points on the line, (1, 45) and (2, 60),

Slope (m) = (60 - 45)/(2 - 1) = 15/1

m = 15

✔️To find b, substitute (x, y) = (1, 45) and m = 15 into y = mx + b.

45 = 15(1) + b

45 = 15 + b

45 - 15 = b

30 = b

b = 30.

✔️To write the equation, substitute m = 15 and b = 30 into y = mx + b

y = 15x + 30

✔️To determine how much Tina will have in her account (y) after 15 weeks (x) of mowing, substitute x = 15 into y = 15x + 30:

y = 15(15) + 30

y = 225 + 30

y = 2

Therefore, Tina will have $255 in her accounts after 15 weeks of mowing lawns.