Question

a line of best fit was drawn to the plotted points in a data set below. based on the line of best fit, for what x - value does y = 17?

Explanation:

Step1: Find the slope of the line

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the points $(0,2)$ and $(12,11)$. Then $m=\frac{11 - 2}{12-0}=\frac{9}{12}=\frac{3}{4}$.

Step2: Find the y - intercept

The equation of a line in slope - intercept form is $y=mx + b$, where $b$ is the y - intercept. Using the point $(0,2)$, when $x = 0$ and $y=2$, we substitute into $y=mx + b$ and get $b = 2$. So the equation of the line of best fit is $y=\frac{3}{4}x+2$.

Step3: Solve for x when y = 17

Substitute $y = 17$ into the equation $y=\frac{3}{4}x+2$. We get $17=\frac{3}{4}x+2$.
Subtract 2 from both sides: $17 - 2=\frac{3}{4}x$, so $15=\frac{3}{4}x$.
Multiply both sides by $\frac{4}{3}$ to solve for $x$: $x=15\times\frac{4}{3}=20$.

Answer:

20