Question

How do you graph $y=8x-7$ ?

Answer 1

In this question, we have to draw the graph of a given equation. 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 $y=8x-7$ --------- (1)
We will apply the substitution method in the above equation, that is
Let x=0 in equation (1), we get
$\begin{aligned} & y=8(0)-7 \\\ & \Rightarrow y=0-7 \\\ \end{aligned}$
Therefore, we get
$\Rightarrow y=-7$
Thus, coordinate will become A(x,y)=A(0,-7)
Let y=0 in equation (1), we get
$0=8x-7$
Now, add 7 on both sides of the equation, we get
$\Rightarrow 0+7=8x-7+7$
As we know, the same terms cancel out with different signs, we get
$\Rightarrow 7=8x$
Now, divide 8 on both sides of the equation, we get
$\begin{aligned} & \Rightarrow \dfrac{7}{8}=\dfrac{8}{8}x \\\ & ~\Rightarrow 0.875=x \\\ \end{aligned}$
Thus, coordinate is B(x,y)=B(0.875,0)
Let x=1 in equation (1), we get
$\begin{aligned} & y=8(1)-7 \\\ & \Rightarrow y=8-7 \\\ \end{aligned}$
Therefore, we get
$\Rightarrow y=1$
Thus, coordinate is C(x,y)=C(1,1)
Let y=-1 in equation (1), we get
$\begin{aligned} & -1=8(x)-7 \\\ & \Rightarrow -1=8x-7 \\\ \end{aligned}$
Now, add 7 on both sides of the above equation, we get
$\Rightarrow -1+7=8x-7+7$
As we know, the same terms cancel out with different signs, we get
$\Rightarrow 6=8x$
Now, divide 8 on both sides of the above equation, we get
$\begin{aligned} & \Rightarrow \dfrac{6}{8}=\dfrac{8}{8}x \\\ & ~\Rightarrow 0.75=x \\\ \end{aligned}$
Thus, coordinate is D(x,y)=D(0.75,-1)
After finding these coordinates A(0,-7), B(0.875,0), C(1,1), and D(0.75,-1), we will plot these points on the graph, that is

After plotting these points, join these points to get a curve of equation $y=8x-7$ .

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.