Question

what is the equation of the line?
○ $y = 3x$
○ $y = \frac{1}{3}x$
○ $y = \frac{1}{3}x + 2$
○ $y = 3x + 2$

Explanation:

Step1: Find the slope

The slope \( m \) is calculated as \( \frac{\text{rise}}{\text{run}} \). From the graph, the rise is 1 and the run is 3, so \( m = \frac{1}{3} \).

Step2: Find the y-intercept

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

Step3: Write the equation

Using the slope-intercept form \( y = mx + b \), substitute \( m = \frac{1}{3} \) and \( b = 2 \), we get \( y = \frac{1}{3}x + 2 \).

Answer:

\( y = \frac{1}{3}x + 2 \) (corresponding to the option \( y=\frac{1}{3}x+2 \))