Question

identify the slope and y - intercept of the line below.
slope =
y - intercept =

Explanation:

Step1: Select two points

Let's take two points on the line, say (-4, 6) and (2, 8).

Step2: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values: $m=\frac{8 - 6}{2-(-4)}=\frac{2}{6}=\frac{1}{3}$.

Step3: Find the y - intercept

The y - intercept is the y - value where the line crosses the y - axis. From the graph, the line crosses the y - axis at the point (0, $\frac{20}{3}$). We can also use the point - slope form $y - y_1=m(x - x_1)$ with the point (-4, 6) and $m = \frac{1}{3}$. $y-6=\frac{1}{3}(x + 4)$, when $x = 0$, $y-6=\frac{4}{3}$, $y=\frac{18 + 4}{3}=\frac{22}{3}$. Another way, using two - point form and converting to slope - intercept form $y=mx + b$. Using points (-4, 6) and (2, 8), first find slope $m=\frac{1}{3}$, then substitute one of the points (e.g., (2, 8)) into $y=mx + b$: $8=\frac{1}{3}(2)+b$, $b=8-\frac{2}{3}=\frac{24 - 2}{3}=\frac{22}{3}$.

Answer:

slope = $\frac{1}{3}$
y - intercept = $\frac{22}{3}$