Question

How do you graph \[2x + y = 5\] by plotting points?

Answer 1

Hint: In this question, we need to plot a graph of the given linear equation. Note that the given equation is a linear equation. To plot the graph, we find the intercepts, so we set one variable to zero and obtain the other variable and vice versa. Firstly, to obtain the \[x\]-intercept, we set the value of y equal to zero and find the point. Then, to obtain the \[y\]-intercept, we set the value of x equal to zero and find the point. Then from obtained \[\left( {x,y} \right)\] points we plot a graph of the given equation in the x-y plane.

Complete step by step solution:
Write the given equation as shown below.
\[2x + y = 5\] …… (1)
We are asked to draw the graph of the above equation.
It is observed that the given equation is one of the equations of a straight line. We know this fact because both x and y terms in the equation are of power 1 (so they are not squared or square rooted terms).
We can simplify the given equation, so that our calculation becomes easier.
We draw the graph by finding \[x\]-intercept and \[y\]-intercept.
So we find the points of intercepts and then draw a line through them.
Finding the \[x\]-intercept:
The line crosses the x-axis at \[y = 0\].
Taking \[y = 0\] in the equation (1) we get,
\[ \Rightarrow 2x + 0 = 5\]
This can be written as,
\[ \Rightarrow 2x = 5\]
Dividing throughout by 3, we get,
\[ \Rightarrow \dfrac{{2x}}{2} = \dfrac{5}{2}\]
\[ \Rightarrow x = \dfrac{5}{2}\]
So the point is \[\left( {\dfrac{5}{2},0} \right)\].
Finding the \[y\]-intercept :
The line crosses the y-axis at \[x = 0\].
Taking \[x = 0\] in the equation (1) we get,
\[ \Rightarrow 2\left( 0 \right) + y = 5\]
This can be written as,
\[ \Rightarrow 0 + y = 5\]
\[ \Rightarrow y = 5\]
So the point is \[\left( {0,5} \right)\].
Hence the \[x\]-intercept is \[\left( {\dfrac{5}{2},0} \right)\] and the \[y\]-intercept is \[\left( {0,5} \right)\].
Now we plot the graph for the obtained points as shown below.

Note that the graph is a straight line.

Note:
We can also plot the graph of the linear equation by using slope and intercept form.
Students must remember that to obtain the \[x\]-intercept, we set the value of y equal to zero and find the point. Then, to obtain the \[y\]-intercept, we set the value of x equal to zero and find the point. Then from obtained \[(x,y)\]points we plot a graph of the given equation in the x-y plane.
Linear graphs have many applications. In our day-to-day life, we observe variation in the value of different quantities depending upon the variation in values of other quantities.
For example, if the number of persons visiting a cloth shop increases, then the earning of the shop also increases and vice versa.