the graph shows a linear relationship between x and y. which equation represents this relationship, where r…

Explanation:

Step1: Find two - point form

First, identify two points on the line from the graph. Let's assume two points ((x_1,y_1)) and ((x_2,y_2)). The general form of a linear equation is (Ax + By=C), which can also be written as (y=mx + b) (slope - intercept form), where (m=\frac{y_2 - y_1}{x_2 - x_1}).

Step2: Use the standard form

The standard form of a linear equation is (Ax+By = C). We can rewrite it as (y=-\frac{A}{B}x+\frac{C}{B}). If we assume the line passes through ((x_1,y_1)) and ((x_2,y_2)), we can substitute into the standard - form equation (Ax + By=C). Let's assume the line passes through ((0,\frac{3}{2})) and ((\frac{3}{2},0)) (by observing the x - intercept and y - intercept from the graph). The slope (m=\frac{0-\frac{3}{2}}{\frac{3}{2}-0}=- 1). The equation of the line in slope - intercept form is (y=-x+\frac{3}{2}), or (2y=-2x + 3), or (2x+2y = 3). If we rewrite the given[SSE Completed, Client Connection Error][SSE onError error]