Q51. - Algebra 2

Question

Graph each inequality.

$y+0.5x<4$

Step-by-Step Solution

Answer

The graph of inequality is as shown.

Step-1 &ndash; convert the given in equation in to equation

$\begin{array}{l}y+0.5x<\mathrm{4.......}\left(1\right)\\ y+0.5x=4\end{array}$

Step-2 &ndash; Solving for point identification

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

$\begin{array}{ccc}x& 0& 8\\ y& 4& 0\end{array}$

Step-3 &ndash; solve to identify the shaded region with respect to origin

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

$\begin{array}{l}y+0.5x<4\\ y+0.5x=4\\ 0+0.5\left(0\right)=4\\ 0+0=4\\ 0<4\end{array}$

$0<4$ It is true, so that shaded region fall towards the origin.

Step-4 &ndash; Plot the graph

Hence, the graph of inequality is as shown.