Question

Graph the inequality on a plane.5y - 6x > 30

Answer 1

The given inequality is:

`5y-6x>30`

It is required to graph the inequality on a plane.

First graph the boundary line by changing the inequality sign to the equal sign:

`5y-6x=30`

Graph the line using two points.

Find y when x=0:

`\begin{gathered} 5y-6(0)=30 \\ \Rightarrow5y-0=30 \\ \Rightarrow5y=30 \\ \Rightarrow(5y)/(5)=(30)/(5) \\ \Rightarrow y=6 \end{gathered}`

Hence, a point on the boundary line is (0,6).

Find x when y=0:

`\begin{gathered} 5(0)-6x=30 \\ \Rightarrow0-6x=30 \\ \Rightarrow-6x=30 \\ \Rightarrow(-6x)/(-6)=(30)/(-6) \\ \Rightarrow x=-5 \end{gathered}`

Hence, another point on the boundary line is (-5,0).

Plot the points on the plane and join them with a line :

A broken line is used because the points on the boundary line are not included in the inequality (the sign '>' is used).

Use a test point (0,0) to check the region to shade.

Substitute (x,y)=(0,0) into the inequality and check if it's true:

`\begin{gathered} 5(0)-6(0)>30 \\ \Rightarrow0-0>30 \\ \Rightarrow0>30 \end{gathered}`

Notice that the inequality is not true.

Hence, plot the test point (0,0) and shade the region that does not contain the test point.

Plot the test point:

Shade the region that does not contain the test point:

The required graph of the inequality is: