Question

question 2
what does the slope of your line tell you about elijahs savings?
elijah is saving up for a new pair of sneakers. he tracks how much money he has in his savings account at the end of each week and plots the data on a scatterplot to see how his savings are growing over time.

Explanation:

Step1: Recall the meaning of slope in a linear relationship

In a linear relationship \(y = mx + b\) (where \(y\) is the amount saved, \(x\) is the week), the slope \(m=\frac{\Delta y}{\Delta x}\). Here, \(\Delta y\) is the change in the amount saved and \(\Delta x\) is the change in the number of weeks.

Step2: Interpret the slope in the context of savings

The slope represents the rate of change of the amount of money saved with respect to time (weeks). A positive slope means that the amount of money in Elijah's savings account is increasing over time. Mathematically, if we consider two points \((x_1,y_1)\) and \((x_2,y_2)\) on the line of best - fit (where \(x\) is the week number and \(y\) is the amount saved), \(m=\frac{y_2 - y_1}{x_2 - x_1}\). The value of the slope tells us how much more money Elijah saves per week.

Answer:

The slope of the line represents the rate at which Elijah's savings increase per week. A positive slope indicates that his savings are growing over time, and the numerical value of the slope would tell us exactly how many dollars he saves each week.