Question

How do you graph $y=6x-1$ ?

Answer 1

Hint:In this question, we have to draw the graph of a given equation. The equation given to us consists of two variables, will we draw a two-dimensional graph. For drawing the graph, we have to use the substitution method to get the values of x and y, so that we can plot a graph. First, we put different values of x in the equation and solve for y. Similarly, we put different values of y in the equation and solve for x. Then, we plot those coordinates in the two-dimensional graph and join all the points to get a required curve or a straight line.

Complete step by step answer:
According to the question, it is given that equation is $y=6x-1$ --------- (1)
We will apply the substitution method in the above equation, that is
Let x=0 in equation (1), we get
$\begin{align}
  & \Rightarrow y=6(0)-1 \\
 & \Rightarrow y=0-1 \\
\end{align}$
Therefore, we get
$\Rightarrow y=-1$
Thus, coordinate will become A(x,y)=A(0,-1)
Let y=0 in equation (1), we get
$\Rightarrow 0=6x-1$
Now, add 1 on both sides of the above equation, we get
$\Rightarrow 0+1=6x-1+1$
As we know, the same terms with different signs cancel out each other, we get
$\Rightarrow 1=6x$
Now, divide 6 on both sides of the equation, we get
$\begin{align}
  & \Rightarrow \dfrac{1}{6}=\dfrac{6}{6}x \\
 & \Rightarrow 0.167=x \\
\end{align}$
Thus, coordinate is B(x,y)=B(0.167,0)
Let x=1 in equation (1), we get
$\begin{align}
  & \Rightarrow y=6(1)-1 \\
 & \Rightarrow y=6-1 \\
\end{align}$
Therefore, we get
$\Rightarrow y=5$
Thus, coordinate is C(x,y)=C(1,5)
Let y=1 in equation (1), we get
$\Rightarrow 1=6x-1$
Now, add 1 on both sides of the above equation, we get
$\Rightarrow 1+1=6x-1+1$
As we know, the same terms with different signs cancel out each other, we get
$\Rightarrow 2=6x$
Now, divide 6 on both sides of the above equation, we get
$\begin{align}
  & \Rightarrow \dfrac{2}{6}=\dfrac{6}{6}x \\
 & \Rightarrow \dfrac{1}{3}=x \\
\end{align}$
Therefore we get
$\Rightarrow 0.34=x$
Thus, coordinate is D(x,y)=D(0.34,1)
After finding these coordinates A(0,-1), B(0.167,0), C(1,5), and D(0.34,1), we will plot these points on the graph, that is

After plotting these points, join these points to get a curve of equation $y=6x-1$ .

Therefore, for the equation $y=6x-1$ , we have plotted the graph using different coordinates.

Note:
Do all the calculations carefully to avoid calculation mistakes. For plotting the graph, atleast find 4 coordinates to get a perfect curve or a straight line. Always mention the points on the graph.