Question

How do you graph \[x - y = 10\]\[?\]

Answer 1

Hint: 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.