Question

a scatter plot includes the following points (0, 1500), (8, 3700)
write the line of best fit (trend line) that contains these points then predict the y value when x = 15
3220
8745
1500
5625

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(0,1500)$ and $(x_2,y_2)=(8,3700)$. So, $m=\frac{3700 - 1500}{8-0}=\frac{2200}{8}=275$.

Step2: Find the y - intercept

The line is in the form $y = mx + b$. When $x = 0$, $y=b$. Since one of the points is $(0,1500)$, the y - intercept $b = 1500$. So the equation of the line is $y=275x + 1500$.

Step3: Predict the y - value

Substitute $x = 15$ into the equation $y=275x + 1500$. Then $y=275\times15+1500=4125 + 1500=5625$.

Answer:

D. 5625