Q49. - Algebra 2

Question

Graph each inequality.
$y\le 3x-5$

Step-by-Step Solution

Answer

The graph of inequality is as shown.

Step-1 – convert the given in equation in to equation

$\begin{array}{l}y\le 3x-\mathrm{5........}\left(1\right)\\ y-3x=3x-5-3x\\ y-3x=-\mathrm{5.........}\left(2\right)\end{array}$

Step-2 – Solving for point identification

To solve the equation by putting the value of given variables one by one zero we get,

$\begin{array}{ccc}x& 0& 5/3\\ y& -5& 0\end{array}$

tep-3 – solve to identify the shaded region with respect to origion

Now, substitute point $\left(0,0\right)$ in first equation we get,

$\begin{array}{l}y\le 3x-5\\ y+3x=-5\\ 0+3\left(0\right)=-5\\ 0\le -5\end{array}$

$0\le -5$ it is not true, so that shaded region fall away from origin

Step-4 – Plot the graph

Hence, the graph of inequality is as shown.