Question

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

Answer 1

The points given to us are: $(x_1,y_1)=(1,2)$ and $(x_2,y_2)=(3,-2)$. To find the line that passes through these points, we will use the formula:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

Thus, employing this formula we get:

$\frac{y-2}{x-1}=\frac{-2-2}{3-1}=\frac{-4}{2}=\frac{x}{y} =-2$

Thus, $\frac{y-2}{x-1}=-2$

$y-2=-2(x-1)$

$y=-2x+2+2=-2x+4$

Thus the slope-intercept form of the line passing through the points (1,2) and (3,-2) is: $y=-2x+4$ 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: $y$. The region that represents the inequality is shown in the graph attached.