Question

Find the plotted yless than or equal to -4x - 1

Answer 1

To find the plot of the inequality:

`y\leq4x-1`

we first need to plot the equation:

`y=4x-1`

To do this we give values to x to get two points. If x=0 then y=-1; if x=1 then y=3. Then we have the points (0,-1) and (1,3). Once we have this points we plot them in the plane and join them with a straigh line:

Now, we need to choose one of the two subplanes that represents tha inequality. To do this we need to take a sample point in one of the subplanes to see if the inequality holds. Choosing the origin (0,0) we get:

`0\leq-1`

since this is not true, therefore the left semiplane does not fullfil the inequality. This means that we have to choose the right semiplane, therefore the graph of the inequality is: