Question

what is the equation of the trend line in the scatter plot?

Explanation:

Step1: Find two points on the trend - line

We can choose the points (0, 7) and (7, 2).

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $(x_1,y_1)=(0,7)$ and $(x_2,y_2)=(7,2)$ gives $m=\frac{2 - 7}{7 - 0}=\frac{-5}{7}=-\frac{5}{7}$.

Step3: Find the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point (0, 7), $b = 7$.

Step4: Write the equation of the line

The slope - intercept form of a line is $y=mx + b$. Substituting $m =-\frac{5}{7}$ and $b = 7$ gives $y=-\frac{5}{7}x+7$.

Answer:

$y =-\frac{5}{7}x + 7$