Question

what are the slope and the y - intercept of the line of best fit on this scatter plot?
a. the y - intercept is 8, and the slope is -\frac{4}{3}
b. the y - intercept is 8, and the slope is \frac{4}{3}
c. the y - intercept is - 8, and the slope is -\frac{4}{3}
d. the y - intercept is 8, and the slope is -\frac{3}{4}

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. The y - intercept is the value of $y$ when $x = 0$.

Step2: Find the y - intercept

From the scatter - plot, when $x = 0$, the line of best fit intersects the y - axis at $y = 8$, so $b=8$.

Step3: Calculate the slope

We can use two points on the line of best fit. Let's use the points $(0,8)$ and $(6,0)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting $x_1 = 0,y_1 = 8,x_2 = 6,y_2 = 0$ into the formula, we get $m=\frac{0 - 8}{6-0}=\frac{-8}{6}=-\frac{4}{3}$.

Answer:

A. The y - intercept is 8, and the slope is $-\frac{4}{3}$