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