Question

the scatter plot shows the number of people in a family and the average amount of money that the family spends on groceries each week. use the equation of the trend line to predict how much money a family with 7 people would spend on groceries each week. a. $210 b. $315 c. $6.43 d. $270

Explanation:

Step1: Find the equation of the trend line

Assume the trend line passes through \((0,0)\) and \((5, 210)\). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{210-0}{5 - 0}=42\). The equation of the line is \(y = 42x\) (using the slope - intercept form \(y=mx + b\), where \(b = 0\) since it passes through the origin).

Step2: Substitute \(x = 7\) into the equation

When \(x = 7\), \(y=42\times7=294\). But looking at the scatter - plot, another way is to observe the pattern. If we note that for \(x = 5\), \(y = 210\) (from the line of best - fit on the scatter - plot), and the line of best - fit seems to have a pattern where when \(x=6\), \(y = 252\) (increase of 42 per unit \(x\)). For \(x = 7\), we can also directly read from the line of best - fit on the scatter - plot. The line of best - fit at \(x = 7\) is at \(y=270\).

Answer:

D. \(\$270\)