Question

what is the slope of line j? thats how much the vertical distance increases for a given increase in the horizontal distance, or the value of vertical distance / horizontal distance. slope = vertical distance / horizontal distance

Explanation:

Step1: Identify vertical and horizontal distances

The two points are $(4,6)$ and $(10,14)$. The horizontal distance (change in $x$) is $10 - 4$, and the vertical distance (change in $y$) is $14 - 6$.

Step2: Calculate the slope

The slope formula is $\text{Slope}=\frac{\text{vertical distance}}{\text{horizontal distance}}=\frac{14 - 6}{10 - 4}$.
$14-6 = 8$ and $10 - 4=6$, so the slope is $\frac{8}{6}=\frac{4}{3}$.

Answer:

$\frac{4}{3}$