Question

1. graph by finding the slope and the y-intercept.

$y = \frac{1}{3}x - 2$
slope (m) =
y-intercept (b) =

Explanation:

Step1: Identify slope from slope-intercept form

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope. For $y = \frac{1}{3}x - 2$, the coefficient of $x$ is the slope.
$m = \frac{1}{3}$

Step2: Identify y-intercept from slope-intercept form

In $y = mx + b$, $b$ is the y-intercept (the point where $x=0$). For $y = \frac{1}{3}x - 2$, the constant term is the y-intercept.
$b = -2$

Step3: Verify graph plotting steps

1. Plot the y-intercept point $(0, -2)$ on the grid.
2. Use the slope $\frac{1}{3} = \frac{\text{rise}}{\text{run}}$: from $(0, -2)$, move up 1 unit and right 3 units to get a second point $(3, -1)$.
3. Draw a straight line through these two points.

Answer:

slope $(m) = \frac{1}{3}$
y-intercept $(b) = -2$
(Graph: Plot $(0, -2)$ and $(3, -1)$, then draw a line through them)