Question

How do you graph the line $2x - 5y = 10$ ?

Answer 1

We must know the coordinates of at least two of the points lying on the line to find the equation of the line. We are given the equation of a line in the question so we will have to find the coordinates using the given equation. To find the coordinates of two points, we have to first put the value of both x and y zero one by one and then find the value of other variables from the equation of the line. By joining these points we can obtain the line on the graph.

Complete step by step answer:
The equation of the line is $2x - 5y = 10$
When $x = 0$
$2(0) - 5y = 10 \\\ \- 5y = 10 \\\ \Rightarrow y = - 2 \\\$
The line cuts the y-axis at the point $(0, - 2)$
When $y = 0$
$2x - 5(0) = 10 \\\ \Rightarrow 2x = 10 \\\ \Rightarrow x = 5 \\\$

The line cuts the x-axis at the point $(5,0)$
Joining these two points and extending the obtained line away in the opposite directions, we can trace the line of the equation $2x - 5y = 10$ .

Note: A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations. We can find the two points by putting random values of one variable and finding out the value of the other variable from the linear equation, but putting the value of each variable zero one by one is more convenient and easy to plot.