Question

How do you graph $$y=5x-2?$$

Answer 1

Hint: The given question describes the operation of addition/ subtraction/ multiplication/ division. Also, this problem involves substituting the $$x$$ values in the given equation to find the value $$y$$. Also, $$y$$ is the function of $$x$$. By using $$x$$ and $$y$$ values we can easily draw the graph for the given equation. We have to assume the value $$x$$ for solving the given question.

Complete step by step solution:
The given equation is shown below,
$$y=5x-2\to \left(1\right)$$
We would draw the graph for the above equation. As a first step, we would assume the $$x$$ value as given below,
$$x=.......-2,-1,0,1,2,.......$$
Let’s substitute $$x=-2$$ in the equation $$\left(1\right)$$, we get
$$\begin{gathered} \left(1\right)\to y=5x-2 \\ y=\left(5\times -2\right)-2 \\ y=-10-2 \\ y=-12 \end{gathered}$$
Let’s substitute$$x=-1$$ in the equation $$\left(1\right)$$, we get
$$\begin{gathered} \left(1\right)\to y=5x-2 \\ y=\left(5\times -1\right)-2 \\ y=-5-2 \\ y=-7 \end{gathered}$$
Let’s substitute $$x=0$$ in the equation $$\left(1\right)$$, we get
$$\begin{gathered} \left(1\right)\to y=5x-2 \\ y=\left(5\times 0\right)-2 \\ y=-2 \end{gathered}$$
Let’s substitute $$x=1$$ in the equation $$\left(1\right)$$, we get
$$\left(1\right)\to y=5x-2$$
$$\begin{gathered} y=\left(5\times 1\right)-2 \\ y=5-2 \\ y=3 \end{gathered}$$
Let’s substitute $$x=2$$ in the equation $$\left(1\right)$$, we get
$$\begin{gathered} \left(1\right)\to y=5x-2 \\ y=\left(5\times 2\right)-2 \\ y=10-2 \\ y=8 \end{gathered}$$
Let’s make a tabular column by using the $$x$$ and $$y$$ values,

$$x$$	$$-2$$	$$-1$$	$$0$$	$$1$$	$$2$$
$$y$$	$$-12$$	$$-7$$	$$-2$$	$$3$$	$$8$$

By using this table we can easily draw the following graph,

The above figure represents the equation $$y=5x-2$$

Note: This type of question involves the operation of addition/ subtraction/ multiplication/ division. In this type of question, we would assume the $$x$$ value, by using the $$x$$ value we can easily find the $$y$$ values. Note that the graph would be based on the equation of $$y$$. $$y$$ is the function of $$x$$ so, $$y$$ can also be written as $$f\left(x\right)$$. When multiplying the different sign numbers remember the following things,
1) When a negative number is multiplied with the negative number the answer becomes a
positive number
2) When a positive number is multiplied with the positive number the answer becomes a
positive number.
3) When a positive number is multiplied with the negative number the answer becomes a
negative number.