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 $y = 13$?

Explanation:

Step1: Find slope from two points

We use points $(4,7)$ and $(8,10)$. Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{10-7}{8-4}=\frac{3}{4}$

Step2: Get line equation (point-slope)

Use point $(4,7)$: $y - 7 = \frac{3}{4}(x - 4)$
Simplify to slope-intercept:
$y = \frac{3}{4}x - 3 + 7$
$y = \frac{3}{4}x + 4$

Step3: Solve for $x$ when $y=13$

Substitute $y=13$ into the equation:
$13 = \frac{3}{4}x + 4$
Subtract 4 from both sides:
$13 - 4 = \frac{3}{4}x$
$9 = \frac{3}{4}x$
Solve for $x$:
$x = 9 \times \frac{4}{3}$

Answer:

$x=12$