Question

the owner of a ramen restaurant records the number of bowls sold and the high temperature each day. the scatter plot shows the data. a good line of fit is drawn through the points (10, 140) and (60, 40).
write the equation of the line of fit.
$y = \square x + \square$

Explanation:

Step1: Calculate the slope

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(10,140)$ and $(60,40)$:
$$m=\frac{40-140}{60-10}=\frac{-100}{50}=-2$$

Step2: Find the y-intercept

Use the slope-intercept form $y=mx+b$, substitute $m=-2$ and point $(10,140)$:
$$140 = -2(10) + b$$
Solve for $b$:
$$140 = -20 + b \implies b=140+20=160$$

Step3: Write the equation

Substitute $m=-2$ and $b=160$ into $y=mx+b$.

Answer:

$y = -2x + 160$