Question

use the graph to find the following. (a) find the slope of the line. 4/3 × (b) is the line increasing or decreasing? increasing decreasing (c) estimate the vertical intercept. (x, y)=(0,2)

Explanation:

Step1: Select two points

Choose two points on the line, say $(- 3,0)$ and $(0,2)$.

Step2: Apply slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $(x_1,y_1)=(-3,0)$ and $(x_2,y_2)=(0,2)$. So $m=\frac{2 - 0}{0-(-3)}=\frac{2}{3}$.

Step3: Determine increasing or decreasing

As $x$ increases, $y$ also increases. So the line is increasing.

Step4: Find vertical intercept

The vertical intercept is the point where the line crosses the $y$-axis. From the graph, it is at $(0,2)$.

Answer:

(a) $\frac{2}{3}$
(b) increasing
(c) $(0,2)$