Question

Draw the graph of the equation $y-2x=4$ and then answer the following,
A. Does the point (2,8) lie on the line? Is (2,8) a solution of the equation? Check by substituting (2,8) in the equation.
B. Does the point (4,2) lie on the line? Is (4,2) a solution of the equation? Check algebraically also.

Answer 1

Hint: we have to draw the equation of line $y-2x=4$ for that we have to find the points A, B, and C by substituting $x=0,1,-2$ in the given equation of line, then we have to plot the points A, B, and C on the graph paper and joint them to get the straight line BC as show in graph sheet. This line is the required graph of the equation $y-2x=4$
Then we plot the point (2,8) on the graph paper and check it by algebraically by putting that points in the given equation $y-2x=4$
Similar, we plot the point (4,2) on the graph paper and check it by algebraically by putting that points in the given equation $y-2x=4$

Complete answer:
Step 1: first of all we have to find the points A, B, and C by substituting $x=0,1,-2$ in the given equation $y-2x=4$
So, by substituting $x=0$ we get,
$$\begin{gathered} \Rightarrow y-2(0)=4 \\ \Rightarrow y=4 \end{gathered}$$
So, we get the point A = $(0,4)$
Step 2: Now, we have to put $x=1$ and find the value of point C as according to the solution step 1. Hence,
$$\begin{gathered} \Rightarrow y-2(1)=4 \\ \Rightarrow y=4+2 \\ \Rightarrow y=6 \end{gathered}$$
Hence, point C is $(1,6)$
Step 3: Now, we have to put $x=-2$ and find the value of point B as according to the solution step 1. Hence,
$$\begin{gathered} \Rightarrow y-2(-2)=4 \\ \Rightarrow y=4-4 \\ \Rightarrow y=0 \end{gathered}$$
Hence, point B is $(-2,0)$
Step 4: Now, we have to draw the graph for all the three points as obtained as A, B, and C in the previous solution steps which is as below:
Step 5: Now, we have to substitute the points $(2,8)$ in the expression $y-2x=4$ so, check that the points satisfy the expression or not. Hence,
$$\begin{gathered} \Rightarrow 8-2(2)=4 \\ \Rightarrow 4=4 \end{gathered}$$
Hence, $(2,8)$ is the solution for the given expression $y-2x=4$ which satisfies the expression.

Step 6: Now, we have to substitute the points $(4,2)$ in the expression $y-2x=4$ so, check that the points satisfy the expression or not. Hence,
$$\begin{gathered} \Rightarrow 4-2(2)=4 \\ \Rightarrow 0\ne 4 \end{gathered}$$
Hence, $(4,2)$ is not the solution for the given expression $y-2x=4$ which does not satisfy the expression.

Final solution: Hence, we have to be satisfied by the graph and by the algebraically that point $(2,8)$ lies on the given equation of line and point $(4,2)$ does not lie on the line.

Note:
We have to find the points A, B and C to plot the graph of the given equation of line $y-2x=4$ we can be determined by substituting $x=0,1,-2$ in the given equation of line.
To satisfy that the points $(2,8)$ and $(4,2)$ lies on the given equation of line $y-2x=4$ by substituting $x=2,y=8$ and $x=4,y=2$ in the given equation of line $y-2x=4$.