Question

8.4.3 test (cst): data and mathematical modeling
estimate the line of best fit using two points on the line.
a. $y = 2x + 10$
b. $y = 10x + 2$
c. $y = 2x$
d. $y = 10x$

Explanation:

Step1: Calculate the slope \(m\)

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given points \((x_1,y_1)=(2,20)\) and \((x_2,y_2)=(8,80)\).
\(m=\frac{80 - 20}{8 - 2}=\frac{60}{6}=10\)

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Substitute \(m = 10\), \(x_1=2\), \(y_1 = 20\) into \(y - y_1=m(x - x_1)\).
\(y-20=10(x - 2)\)
Expand: \(y-20=10x-20\)
Add 20 to both sides: \(y=10x\)

Answer:

D. \(y = 10x\)