Question

Sketch a graph of −3x − y = −4

Answer 1

First we notice that the equation is linear which means that its graph will be a line. To graph the equation we first solve it for y:

`\begin{gathered} -3x-y=-4 \\ y=-3x+4 \end{gathered}`

Once we have the expression for y we give values to x (whichever value we want) and find its corresponding y using the equation above, this will give us points on the graph of the equation. For example, if x=0 we have:

`\begin{gathered} y=-3\left(0\right)+4 \\ y=0+4 \\ y=4 \end{gathered}`

Hence, the graph passes through the point (0,4).

Following the same approach we can find various points on the graph, some of them are shown in the table below:

Now we plot this points on the plane and then we join them with a straight line. Therefore, the graph of the equations is: