Question

graph with a coordinate grid (chart) showing a line. below the graph: (a) ( y = -2x - 3 ); (b) ( y = \frac{1}{2}x - 3 ); (c) ( y = 2x - 3 ) (circled); (d) ( y = 2x + 3 ).

Explanation:

Step1: Identify two points on the line

From the graph, we can see that the line passes through \((0, -3)\) (the y-intercept) and \((1, -1)\) (or other points, but let's use these for simplicity).

Step2: Calculate the slope \(m\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((x_1,y_1)=(0, - 3)\) and \((x_2,y_2)=(1, - 1)\), we get \(m=\frac{-1-(-3)}{1 - 0}=\frac{2}{1} = 2\).

Step3: Determine the equation of the line

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We know \(m = 2\) and from the point \((0,-3)\), \(b=-3\). So the equation of the line is \(y = 2x-3\).

Answer:

\(y = 2x - 3\) (corresponding to option C)