Question

the scatter plot shows the scores that several students made on their math semester exam and their science semester exam. use the equation of the trend line to predict the science exam score of someone who scored an 84 on their math exam. a. 94 b. 73 c. 63 d. 99

Explanation:

Step1: Find two points on the trend line

Let's take two points \((40,40)\) and \((60,50)\) from the trend - line.

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting \(x_1 = 40,y_1 = 40,x_2=60,y_2 = 50\), we get \(m=\frac{50 - 40}{60 - 40}=\frac{10}{20}=0.5\).

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((40,40)\) and \(m = 0.5\), the equation is \(y-40=0.5(x - 40)\).
Simplify it: \(y-40=0.5x-20\), so \(y = 0.5x+20\).

Step4: Substitute \(x = 84\) into the equation

When \(x = 84\), \(y=0.5\times84 + 20\).
\(y=42+20=62\approx63\) (due to possible approximation in reading the trend - line points).

Answer:

C. 63