The graph below shows a line segment pq: graph of line pq going through ordered pairs negative 1, 3 and 2, negative 3 which of the following equations best represents the line segment pq? a: y = −3x + 2b: y = −2x + 1c: y = −3x − 2d: y = −2x − 1

You actually don't need a graph to be able to solve this equation. As long as you are given two data points, you can already solve for the linear equation.

The most common way of writing linear equations is the slope-intercept form:
y = mx + b, where m is the slope and b is the y-intercept.

The slope is the ratio of the change of y to the change of x coordinates. Let's say point 1 is (-1,3) and point 2 is (2,-3). Then,

m = (-3-3)/(2-⁻1) = -2

Next, we use any of the given point to the standard equation along with the m to find b. Let's use (-1,3)

3 = -2(-1)+b
b = 1

Thus, the complete linear equation is y = -2x + 1. The answer is B.