Write the slope-intercept inequality for the graph below (1,2) (3,-2)

The points given to us are: [tex] (x_1,y_1)=(1,2) [/tex] and [tex] (x_2,y_2)=(3,-2) [/tex]. To find the line that passes through these points, we will use the formula:[tex] \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} [/tex]Thus, employing this formula we get:[tex] \frac{y-2}{x-1}=\frac{-2-2}{3-1}=\frac{-4}{2}=\frac{x}{y} =-2 [/tex]Thus, [tex] \frac{y-2}{x-1}=-2 [/tex][tex] y-2=-2(x-1) [/tex][tex] y=-2x+2+2=-2x+4 [/tex]Thus the slope-intercept form of the line passing through the points (1,2) and (3,-2) is: [tex] y=-2x+4 [/tex] and is depicted by the dotted line in the graph attached. Now, since we want the slope-intercept inequality for the graph below the points (1,2) and (3,-2), we will write the inequality as: [tex] y<-2x+4 [/tex]. The region that represents the inequality is shown in the graph attached.