Select the inequalities represented by the graph below. Select all that apply.

First we find the equation of the line. Notice that the line goes through the point (0,c). Since c is on the y-axis, c is the y-intercept. To find the slope take any two points and count the boxes (up or down) from one to the other. Divide that by the number of boxes (left and right) from one to the other. I chose (0,c) and (1,-1) so I traveled down 2 and right 1. Down (negative) 2 and right (positive) 1 gives me a slope of -2/1 = -2.

The equation of a line is given by y = my +b where m is the slope (here -2) and b is the y-intercept (here c). That makes the equation of the line y=-2x+c.

The shading occurs above the line so we use either greater than (>) or the greater than or equal to sign [tex]( \geq )[/tex]. The way we decide is whether the line is solid (as it is here) or dashed. Here it is solid so we use greater than or equal to.

That makes the correct answer the 5th choice from the top: [tex]y \geq -2x+c[/tex]