Question

How do you graph $y=2x-9$?

Answer 1

Hint: Suppose an equation of straight line to be $y=ax+b$. We can draw the graph of $y=ax+b$ from the simple graph $y=x$. We need to modify the $y=x$ graph by shifting and scaling methods. It is a better idea to modify the graph of $y=x$ in such a manner that we get the required graph by going from left side to right side of the equation $y=2x-9$.

As per the given question, we need to graph a straight line which is given by the equation $y=2x-9$.
A straight line can be traced out on the cartesian plane by just two points lying on it. We can also use a third point for sort of check. It is very simple to graph the $y=x$ line as it is symmetric to both x and y axes.

The graph of $y=x$ is as shown in below figure:

If we go from left hand side to right hand side of the equation $y=2x-9$, it is clear that we need to first scale the $y=x$ graph by a factor 2. Then we get, $y=2x$.
And the graph of $y=2x$ is as shown in the below figure:

Now, we need to shift the $y=2x$ graph right hand side by $\dfrac{9}{2}$ units to get the required straight line $y=2x-9$. And the graph of $y=2x-9$ is shown in the below figure:

$\therefore$ We have to compress $y=x$ by 2 and then shift it to the right hand side by $\dfrac{9}{2}$ units to get the desired line $y=2x-9$.

Note:
We can trace the graph of $y=2x-9$ by substitution by any two random values of x. We can also trace the graph by going from the right hand side to left hand side of the straight-line equation $y=2x-9$. So, by taking 2 common, we get $y=2(x-\dfrac{9}{2})$. That is, we have to shift the $y=x$ graph by $\dfrac{9}{2}$ units and then compress it by a factor 2 to get the graph of $y=2x-9$.