Question

Draw the graph of the equation \[y-2x=4\] and then answer the following.
1. 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.
2. Does the point (4,2) lie one the line? is (4,2) a solution of the equation? Check algebraically also.

Answer 1

Hint: We have to draw the graph using x=0 and then y=0 to get the desired points and then we check if the given points in (i) and (ii) are satisfied by the given equation.

Complete step-by-step answer:
To draw the graph, we see possible point of x when y is put to be 0 and similarly, we see the possible points of y when x is put to be 0
Equation is \[y-2x=4\]………(i),
putting y=0 in equation (i) we get
 \[-2x=4\]
\[\Rightarrow x=-\dfrac{4}{2}=-2\]
Similarly, putting x=0 in equation (i) we get \[y=4\].

Then the possible points are \[(-2,0)\] and \[(0,4)\], using these values to make the graph we get graph as


Now we will proceed to answer the question given in points:
(i)To check if the point \[(2,8)\] is the solution of the equation there are two methods either we check if the point \[(2,8)\] lies on the line or it satisfies the given equation \[y-2x=4\]. The later can be done by substituting point \[(2,8)\] in the equation \[y-2x=4\]

Putting x=2 and y=8 in left hand side of the equation \[y-2x\] we get \[8-4=4\], which is equal to the Right hand side of the equation, so the point \[(2,8)\] satisfies the given equation \[y-2x=4\]. Also, because the point \[(2,8)\] satisfies the given equation \[y-2x=4\], so it lies on the line. Graph of it is as below:

(ii) We have to do a similar procedure to check if \[(4,2)\] satisfies the given equation.
Substituting x=4 and y=2 in the left hand side of the equation\[y-2x=4\] we get \[2-8=-6\] which is not equal to the right hand side of the given equation.
Hence, the \[(4,2)\] point does not satisfy the given equation \[y-2x=4\]. Also, because the point \[(4,2)\] does not satisfy the given equation \[y-2x=4\], so it does not lie on the line. Graph of it is as below:

Note: Always verify that the given points in (i) and (ii) satisfy the given equation \[y-2x=4\] by substituting the values of x and y in the L.H.S. of the equation and then proceed for graphing of the points.