Question

given the scatter plot below, write the equation for the line of best fit in slope - intercept form.

Explanation:

Step1: Identify two points on line

Let's take two points on the line of best - fit, say $(0, - 5)$ and $(-2,5)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points $(x_1,y_1)=(0, - 5)$ and $(x_2,y_2)=(-2,5)$ gives $m=\frac{5-(-5)}{-2 - 0}=\frac{10}{-2}=-5$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,-5)$, $b=-5$.

Step4: Write the equation

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

Answer:

$y=-5x - 5$