Question

How do you graph the line $y=\dfrac{5}{3}x$?

Answer 1

Hint: In this question, we are given an equation of line and we need to draw it on the graph. For this, we will try to find coordinates of some points on the line. We will suppose some value of x and find the corresponding value of y. We will get points in the form as (x,y). We will plot these points on the line and then draw a line joining these points which will be the required line on the graph.

Complete step by step answer:
Here we are given the equation of line as $y=\dfrac{5}{3}x$.
We need to draw this line on the graph. For this let us first find coordinates of some point that lie on the line $y=\dfrac{5}{3}x$.
For this we will suppose some value of x and find the corresponding value of y. This will give us the coordinates of the point in the form (x,y) which can be plotted easily on the graph. As we know that, only two points are sufficient to draw a straight line. So let us find the coordinate of two points on which the line lies.
We can see that if we put the value of x as 1 or 2, the value of y will be a fraction which is difficult to plot. For ease let us put the value of x as 3 or multiple of 3 so that it cancels out with the 3 in the denominator and gives us the value of y as integer.
So let us put the value of x as 3 we get $y=\dfrac{5}{3}\times 3$.
Cancelling 3 by 3 we get y = 5. So our point becomes (3,5).
Now let us put the value of x as -3 we get $y=\dfrac{5}{3}\times \left( -3 \right)$.
Simplifying we get $y=\dfrac{-5}{3}\times 3$.
Cancelling 3 by 3 we get y = -5. So our point becomes (-3,-5).
Now let us draw the axis on a graph and mark the required points. Then let us plot these points. At last let us draw a line passing through these points. This line is the required line on the graph. The graph looks like this,

Note: Students should take care of the signs in coordinates of the point. Take care of points on the negative and positive axis. Make the axis properly where X is the positive x axis, X' is the negative x axis, Y is the positive y axis and Y' is the negative y axis.