Question

use this equation to draw a graph y>-5/3x-4

Answer 1

Given:

$y>-\frac{5}{3}x-4$

To draw the given inequality, we need to draw the line:

$y=-\frac{5}{3}x-4$

To draw the line, we need two points

Substitute with x = 0 and 3 and find the corresponding value of y

So,

$\begin{gathered} x=0\rightarrow y=-\frac{5}{3}\cdot0-4=-4 \\ x=3\rightarrow y=-\frac{5}{3}\cdot3-4=-5-4=-9 \end{gathered}$

so, the line passes through the points (0, -4) and (3, -9)

We will check which side of the line is the solution using the point (0,0)

So,

$\begin{gathered} -\frac{5}{3}\cdot0-4=-4<0 \\ 0>-4 \end{gathered}$

So, the area contains the point (0, 0) is the area of the solution

The graph will be as shown in the following picture: