Question

the graph of a line passes through the points (0, -2) and (6, 0). what is the equation of the line?
y = -2x + 6
y = \frac{1}{3}x - 6
y = 3x - 2
y = \frac{1}{3}x - 2

Explanation:

Step1: Calculate slope of the line

The slope $m$ between points $(x_1,y_1)=(0,-2)$ and $(x_2,y_2)=(6,0)$ is given by:
$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-2)}{6-0}=\frac{2}{6}=\frac{1}{3}$$

Step2: Identify y-intercept

The line passes through $(0,-2)$, so the y-intercept $b=-2$.

Step3: Write line equation

Using slope-intercept form $y=mx+b$:
$$y=\frac{1}{3}x-2$$

Answer:

$\boldsymbol{y=\frac{1}{3}x-2}$ (the bottom-right option)