Question

what is the equation of the line shown below? select the correct answer $y = \frac{1}{3}x - 2$ $y = -\frac{3}{4}x + 2$ none of the answers $y = \frac{1}{3}x + 2$

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at (0, 2), so the y-intercept \( b = 2 \). The slope-intercept form is \( y = mx + b \), so the equation should have \( +2 \) at the end. This eliminates the first option (\( y = \frac{1}{3}x - 2 \)) and the second option has a negative slope, but the line is increasing (positive slope), so eliminate \( y = -\frac{3}{4}x + 2 \).

Step2: Determine the slope

The line passes through (0, 2) and let's find another point. From (0, 2), moving 3 units right (x increases by 3) and 1 unit up (y increases by 1) gives (3, 3). The slope \( m = \frac{\Delta y}{\Delta x} = \frac{1}{3} \). So the equation is \( y = \frac{1}{3}x + 2 \).

Answer:

\( y = \frac{1}{3}x + 2 \) (the fourth option: \( y = \frac{1}{3}x + 2 \))