Question

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

Answer 1

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

$$\left( 1 \right) \to y = 5x - 2 \\\ y = \left( {5 \times - 2} \right) - 2 \\\ y = - 10 - 2 \\\ y = - 12 \\\$$

Let’s substitute$x = - 1$ in the equation $\left( 1 \right)$, we get

$$\left( 1 \right) \to y = 5x - 2 \\\ y = \left( {5 \times - 1} \right) - 2 \\\ y = - 5 - 2 \\\ y = - 7 \\\$$

Let’s substitute $x = 0$ in the equation $\left( 1 \right)$, we get

$$\left( 1 \right) \to y = 5x - 2 \\\ y = \left( {5 \times 0} \right) - 2 \\\ y = - 2 \\\$$

Let’s substitute $x = 1$ in the equation $\left( 1 \right)$, we get
$\left( 1 \right) \to y = 5x - 2$

$$y = \left( {5 \times 1} \right) - 2 \\\ y = 5 - 2 \\\ y = 3 \\\$$

Let’s substitute $x = 2$ in the equation $\left( 1 \right)$, we get

$$\left( 1 \right) \to y = 5x - 2 \\\ y = \left( {5 \times 2} \right) - 2 \\\ y = 10 - 2 \\\ y = 8 \\\$$

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.