Question

Write the slope-intercept inequality for the graph below. If necessary, use <=for < or >= for 2.• (0.4)(-3,0)-5

Answer 1

Answer::

`y\ge(4)/(3)x+4`

Step-by-step explanation:

The first step is to determine the equation of the boundary line in slope-intercept form.

Find the slope of the line using the points (0,4) and (-3,0).

`\begin{gathered} \text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =(0-4)/(-3-0) \\ =(-4)/(-3) \\ m=(4)/(3) \end{gathered}`

The line intersects the y-axis at (0,4).

• Thus, y-intercept, b=4

Substitute into the slope-intercept form: y=mx+b

`y=(4)/(3)x+4`

This is the equation of the boundary line.

Next, we place the inequality.

• The boundary line is ,an unbroken line,, the possible inequalities are: ≤ or ≥

,

• Since the shaded region is ,above the boundary line,, the inequality sign is ≥ (greater than or equal to).

Thus, the slope-intercept inequality for the graph is:

`y\ge(4)/(3)x+4`