Question

Need help figuring out . suppose it passes through (0,-2) and (9.5,0)

Answer 1

Lets suppose tha the graph passes through points

$\begin{gathered} (x_1,y_1)=(0,-2) \\ \text{and} \\ (x_2,y_2)=(9.5,0) \end{gathered}$

Then, the slope of the dashed line is given by

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-2)}{9.5-0}$

which gives

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{2}{9.5}=0.21052$

Then, we can write

$y=mx+b\Rightarrow y=0.21052x+b$

where the y-intercept can be founded by substituting the first point, that is,

$\begin{gathered} -2=0.21052(0)+b \\ b=-2 \end{gathered}$

Then, the dashed line has equation

$y=0.21052x-2$

Finally, since the values of the red region are above the dashed line then, the inequality which represents the red region is:

$y>0.21052x-2$