Chapter 1, Problem 1RE

Graph each equation in Exercises 1-4. Let $x=-3,-2,-1,0,1,2,and3.$

$y=2x-2$

To determine

To graph: The provided equation $y=2x-2$ for $x=-3,-2,-1,0,1,2,3$.

Explanation of Solution

Given Information:

The provided function is $y=2x-2$.

Graph:

Consider the provided function,

$y=2x-2$

Now, choose the values for $x$ and compute the value for $y=2x-2$, in order to form the ordered pairs to plot on the graph.

So, put $x=-3$ in the provided equation $y=2x-2$,

$\begin{array}{c}y=2\left(-3\right)-2\\ =-8\end{array}$

Put $x=-2$ in the provided equation $y=2x-2$,

$\begin{array}{c}y=2\left(-2\right)-2\\ =-6\end{array}$

Put $x=-1$ in the provided equation $y=2x-2$,

$\begin{array}{c}y=2\left(-1\right)-2\\ =-4\end{array}$

Now, put $x=0$ in the provided equation $y=2x-2$,

$\begin{array}{c}y=2\left(0\right)-2\\ =-2\end{array}$

Now, put $x=1$ in the provided equation $y=2x-2$,

$\begin{array}{c}y=2\left(1\right)-2\\ =0\end{array}$

Put $x=2$ in the provided equation $y=2x-2$,

$\begin{array}{c}y=2\left(2\right)-2\\ =2\end{array}$

Put $x=3$ in the provided equation $y=2x-2$,

$\begin{array}{c}y=2\left(3\right)-2\\ =4\end{array}$

The required table is shown below,

$\begin{array}{ccc}x& y& \left(x,y\right)\\ -3& -8& \left(-3,8\right)\\ -2& -6& \left(-2,-6\right)\\ -1& -4& \left(-1,-4\right)\\ 0& -2& \left(0,-2\right)\\ 1& 0& \left(1,0\right)\\ 2& 2& \left(2,2\right)\\ 3& 4& \left(3,4\right)\end{array}$

Plot the above points gives the graph of the given equation. Therefore, the graph of the function $y=2x-2$ as shown below,

Interpretation:

From the graph it can be interpret that this is the graph of straight line whose $x\text{and}y$ intercepts are $\left(1,0\right)\text{and}\left(0,-2\right)$ respectively.