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::

$y\ge\frac{4}{3}x+4$

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).

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

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

• Thus, y-intercept, b=4

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

$y=\frac{4}{3}x+4$

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:

$y\ge\frac{4}{3}x+4$