Question

Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for sor">=" for >.5(-3,0)5(0, -3)

Answer 1

we need to find the line equation for the dashed line. Since we have 2 points of the line, its slope is

`\begin{gathered} m=(-3-0)/(0-(-3)) \\ m=(-3)/(3) \\ m=-1 \end{gathered}`

where we used the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Then, our searched line has the form:

`y=-x+b`

where b is the y-intercept. We can finde b by substituting point (0,-3) into the last equation:

`\begin{gathered} -3=-(0)+b \\ b=-3 \end{gathered}`

then, the searched line in slope-intercept form is

`y=-x-3`

Therfore, the given area can be modeled as

`y>-x-3`

because when a line is dashed it doesn't belong to the given area.