Question

what is the equation of the line graphed?

y
x
\\( y = -\frac{2}{3}x - 2 \\)
\\( y = -\frac{3}{2}x - 2 \\)
\\( y = \frac{2}{3}x - 2 \\)
\\( y = \frac{2}{3}x + 2 \\)

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, -2)$, so $b=-2$.

Step2: Calculate slope

Use two points: $(0, -2)$ and $(3, -4)$.
Slope $m=\frac{-4 - (-2)}{3 - 0}=\frac{-2}{3}=-\frac{2}{3}$

Step3: Write line equation

Substitute $m$ and $b$ into $y=mx+b$:
$y = -\frac{2}{3}x - 2$

Answer:

$y = -\frac{2}{3}x - 2$