Question

Graph the inequality on the axes below.y < -3x - 8

Answer 1

Given the linear inequality;

`y<-3x-8`

We shall find a pair of coordinates that satisfy this inequality. Ordinarily, the sets of coordinates is limitless. However, in order not to spend all day, we can simply use what is commonly refered to as the intercept method.

We shall find the value of y when x = 0, and also the value of x when y = 0.

The first pair of coordinates are thus calculated as shown;

`\begin{gathered} \text{When x}=0 \\ y=-3x-8 \\ y=-3(0)-8 \\ y=0-8 \\ y=-8 \\ We\text{ now have the x and y coordinates for the first point as} \\ (0,-8) \end{gathered}`

For the second pair of coordinates;

`\begin{gathered} \text{When y}=0 \\ y=-3x-8 \\ 0=-3x-8 \\ \text{Add 3x to both sides} \\ 3x=-8 \\ \text{Divide both sides by 3} \\ x=-(8)/(3) \\ x=-2.67 \end{gathered}`

However, to make things easier, since we have a decimal/fraction to deal with on a graph page (which is rather clumsy), we shall take another value of y, that would make x a whole number. Let us take y = -5. We now have;

`\begin{gathered} y=-3x-8 \\ -5=-3x-8 \\ Collect\text{ all like terms and we'll have;} \\ 3x=-8+5 \\ 3x=-3 \\ \text{Divide both sides by 3;} \\ x=-1 \\ \text{The other set of coordinates is;} \\ (-1,-5) \end{gathered}`

Plotting these on a graph page now gives the following graph;

Note however that what we have here is an inequality, which means the values that satifies this inequality does not lie on that line but rather on either side of it. The inequality is given as;

`y<-3x-8`

This reads, "y is less than..."

That implies that the values of y all lies on the left side of the graph, where the values are less than. We now have the shaded region showing all the possible solutions as given below;

To show the points Calculated on the graph;