Q32. - Algebra 2

Question

Graph all points on the coordinate plane to the below the graph of $y=3x-5$ and write an inequality to describe these points

Step-by-Step Solution

Answer

The graph of the inequality is

The inequality is $y<3x-5$

Step-1 &ndash; Apply the concept of plotting graph

Here we have to represent the regions below the graph of the equation $y=3x-5$

The region which is below the graph of the equation will be

$y<3x-5$

Step-2 &ndash; Plot the graph of the given function

The graph can be plot in inequality and it is shown in form of area under the shaded region as follows:

Step-3 &ndash; Describe the points which satisfy the inequality

Consider boundary here is of graph $y<3x-5$Here the inequality sign is less than since, the boundary is dashed.

Let the origin point $\left(0,0\right)$

On substituting the value

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

Thus, the inequality is not true and it does not satisfy the inequality Therefore, shaded region not containing the point $\left(0,0\right)$ all point lying below the dashed boundary satisfies the inequality.