Question

1. write the equation of the line that is graphed below.

Explanation:

Step1: Identify slope and y-intercept

From the graph, the line crosses the y - axis at (0, 3), so the y - intercept \(b = 3\). To find the slope \(m\), we can use two points. We have (0, 3) and (2, - 1). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting the points: \(m=\frac{-1 - 3}{2 - 0}=\frac{-4}{2}=-2\).

Step2: Write the equation

The slope - intercept form of a line is \(y = mx + b\). Substituting \(m=-2\) and \(b = 3\), we get \(y=-2x + 3\).

Answer:

\(y=-2x + 3\)