Question

How do you graph the linear equation $3x + y = 15$?

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 $(x,y)$ points we plot a graph of the given equation in the x-y plane.

Complete step-by-step solution:
Given an equation of the form $3x + y = 15$ …… (1)
We are asked to draw the graph of the above equation.
Note 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 3x + 0 = 15$
This can be written as,
$ \Rightarrow 3x = 15$
Dividing throughout by 3, we get,
$ \Rightarrow \dfrac{{3x}}{3} = \dfrac{{15}}{3}$
$ \Rightarrow x = 5$
So the point is $(5,0)$.
Finding the $y$-intercept :
The line crosses the y-axis at $x = 0$.
Taking $x = 0$ in the equation (1) we get,
$ \Rightarrow 3(0) + y = 15$
This can be written as,
$ \Rightarrow 0 + y = 15$
$ \Rightarrow y = 15$
So the point is $(0,15)$.
Hence the $x$-intercept is $(5,0)$ and the $y$-intercept is $(0,15)$.
Now we plot the graph for the obtained points.
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.
Another example, if a number of people are employed, then the time taken to accomplish a job decreases.
We generally represent this with the help of linear graphs.