Question

ich equation matches this graph?
the graph is a coordinate plane with a line. the options are:
y= 1/2x -2
y= 2x - 2
y=2x+1
y= 1/2x +2
13 of 16

Explanation:

Step1: Identify slope and intercept

The graph crosses the y - axis at (0, - 2), so the y - intercept \(b=-2\). To find the slope, use two points, e.g., (0, - 2) and (4, 0). Slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0-(-2)}{4 - 0}=\frac{2}{4}=\frac{1}{2}\).

Step2: Match with equation

The slope - intercept form is \(y = mx + b\). With \(m=\frac{1}{2}\) and \(b=-2\), the equation is \(y=\frac{1}{2}x-2\).

Answer:

\(y=\frac{1}{2}x - 2\) (the orange - colored option)