Question

How do you graph x - y = 10$$$$?

Answer 1

The given question describes the arithmetic operation of addition/ subtraction/ multiplication/ division. We need to know how to find the value of $y$ from the above equation. Also, this problem involves substituting $x$ values in the given equation to find the value $y$. By using $x$ and $y$ values we would draw the graph.

Complete step by step solution:
The given equation is shown below,
$x - y = 10$
The above equation can also be written as,
$y = x - 10 \to \left( 1 \right)$
We would draw the graph for the above equation. As a first step, we would assume $x$ values as given below,
$x = ..... - 2, - 1,0,1,2,.....$
By substituting the $x$ values in the equation $\left( 1 \right)$, we can find the $y$ values.
Let’s substitute $x = - 2$ in the equation $\left( 1 \right)$, we get
$\left( 1 \right) \to y = x - 10$

$$y = - 2 - 10 \\\ y = - 12 \\\$$

When $x = - 2$ the value of $y$ is $- 12$
Let’s substitute $x = - 1$ in the equation $\left( 1 \right)$, we get
$\left( 1 \right) \to y = x - 10$

$$y = - 1 - 10 \\\ y = - 11 \\\$$

When $x = - 1$ the value of $y$ is $- 11$
Let’s substitute $x = 0$ in the equation $\left( 1 \right)$, we get
$\left( 1 \right) \to y = x - 10$

$$y = 0 - 10 \\\ y = - 10 \\\$$

When $x = 0$ the value of $y$ is $- 10$
Let’s substitute $x = 1$ in the equation $\left( 1 \right)$, we get
$\left( 1 \right) \to y = x - 10$

$$y = 1 - 10 \\\ y = - 9 \\\$$

When $x = 1$ the value of $y$ is $- 9$
Let’s substitute $x = 2$ in the equation $\left( 1 \right)$, we get
$\left( 1 \right) \to y = x - 10$

$$y = 2 - 10 \\\ y = - 8 \\\$$

When $x = 2$ then the value of $y$ is $- 8$
Let’s make a tabular column by using the $x$ and $y$ values.

$x$	$- 2$	$- 1$	$0$	$1$	$2$
$y$	$- 12$	$- 11$	$- 10$	$- 9$	$- 8$

By using these points we can easily draw the graph,

The above graph represents the equation $y = x - 10$

Note: $y$ is the function of $x$ so it can also be written as $f\left( x \right)$. Also, this type of question involves the arithmetic operations like addition/ subtraction/ multiplication/ division. For finding the value of $y$ point we can assume the $x$ values. Note that if an equation is in the form of $y = mx + c$, the graph always will be a straight line.