Shayne wants to earn money to attend a basketball camp. For her 8th-grade graduation, her grandmother gave her part of the money she needs. Every month since then, Shayne has been saving the same amount from her babysitting jobs. After 3 months she had $155, and after 7 months she had $295. Which equation describes the relationship between x, the number of months Shayne has been saving, and y, the amount she has saved?
y = m x + b
295 = m * 7 + b
155 = m * 3 + b
------------------subtract
140 = 4 m
m = 35
so
y = 35 x + b
now put a point in
155 = 35(3) + b
b = 155 - 105
b = 50
so
y = 35 x + 50
To determine the equation that describes the relationship between x (the number of months Shayne has been saving) and y (the amount she has saved), we can use the given information.
Let's break down the problem step-by-step:
1. We know that after 3 months of saving, Shayne had $155.
2. We also know that after 7 months of saving, Shayne had $295.
To find the equation, we need to determine the rate at which Shayne saves money per month.
If Shayne had $155 after 3 months, we can say that she saved a certain amount (let's call it "a") for each of those 3 months. So, after 3 months, the equation can be written as:
3a = 155
Simplifying this equation, we have:
a = 155/3
Using the same logic, after 7 months, the equation can be written as:
7a = 295
Simplifying this equation, we have:
a = 295/7
We now have two different values of "a" from the given information.
To find the equation that describes the relationship between x and y, we need to find a pattern between the number of months and the amount saved.
Since Shayne saves the same amount each month, we can conclude that the equation is linear. This means that the equation follows the form: y = mx + b, where "m" is the slope and "b" is the y-intercept.
Let's represent "a" as the slope "m." Now our two equations are:
y = (155/3)x
y = (295/7)x
These equations represent the relationship between the number of months Shayne has been saving (x) and the amount she has saved (y).