Question

A graph of a linear equation passes through (-2,6) and (0,-6).1. Use the two points to sketch the graph of the equation.2. is 3x-y=-6. an equation for this graph? Explain how you know.

Answer 1

1. To graph this line with the points, we just have to locate these two points and then draw a line that joins them. This is the graph for this line:

2. To see if 3x - y = -6 is an equation for this graph, we can take the points and replace x and y and see if they satisfy the equation:

`\begin{gathered} 3x-y=-6 \\ \text{ for the first point (-2,6):} \\ 3\cdot(-2)-6=-6 \\ -6-6=-6 \\ -12=-6\leftarrow\text{ this equality is false. This point does not satisfy the equation} \\ \text{ for the second point (0, -6)} \\ 3\cdot0-(-6)=-6 \\ 6=-6\leftarrow\text{ this equality is false. This point does not satisfy the equation} \end{gathered}`

Since none of the points satisfy the equation, we can say that this is not an equation for this graph. In fact, the graph of this equation is shown in green in the following diagram:

We can see that the slope is positive, while in our line the slope is negative. Therefore, this can't never be the equation for the graph.