Question

1. write an equation of the graph.

options:
y = 2x - 4
y = 1/2x - 4
y = 1/2x + 2
y = -4x + 2

Explanation:

Step1: Identify the y-intercept

The graph 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 options with \( -4 \) as the constant term (first three wrong constant, wait: first option \( y = 2x - 4 \) (b=-4), second \( y = \frac{1}{2}x - 4 \) (b=-4), third \( y = \frac{1}{2}x + 2 \) (b=2), fourth \( y = -4x + 2 \) (b=2). Now check slope.

Step2: Calculate the slope

Take two points, e.g., (0, 2) and (2, 3). The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 2}{2 - 0} = \frac{1}{2} \). So the slope \( m = \frac{1}{2} \) and y-intercept \( b = 2 \), so the equation is \( y = \frac{1}{2}x + 2 \).

Answer:

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