Question

How do you graph the line$y = 2x - 7$?

Answer 1

Hint:In order to graph the above linear equation having two variables $x\,and\,y$,use the fact that that graph to the equation of the form $ax + by + c = 0$ is always a straight line and to graph a straight line we must requires at least two coordinates.
So,1 st coordinate will be our y-intercept obtained by putting $x = 0$in the equation and 2 nd coordinate by taking $x = 3$.

Complete step by step solution:
We are given an equation that is a linear equation in two variables , here we are having variable $x$and $y$telling. $y = 2x - 7$
So what we are going to do in this question, we are jumping on the cartesian plane.
There is one most important property of the plane which we have to remember while plotting our equation that graphs to any linear equation in two variables of the form $ax + by + c = 0$ will be straight line.
So, in order to draw a line, we must have at least two points on the graph which we can connect to form a line.
To find y-intercept make $x = 3$ in the equation
$
y = 2x - 7 \\
y = 2(3) - 7 \\
y = - 1 \\
$
Now taking $x = 0$
$
y = 2x - 7 \\
y = 2(0) - 7 \\
y = - 7 \\
\\
$
Forming the table of ordered pair of points
x 3 0
y -1 -7
Now plotting points $\left( {3, - 1} \right)$and $\left( {0, - 7} \right)$and connecting them to form the line of the equation $y = 2x - 7$.

Hence, we’ve successfully plotted our graph of $y = 2x - 7$

Note:1. Cartesian Plane: A Cartesian Plane is given its name by the French mathematician Rene Descartes who first used this plane in the field of mathematics .It is defined as the two mutually perpendicular number line , the one which is horizontal is given name x-axis and the one which is vertical is known as a y-axis. With the help of these axes we can plot any point on this cartesian plane with the help of an ordered pair of numbers.

2.Draw the cartesian plane only with the help of a straight ruler and pencil to get the perfect and accurate results.

3.You can take any two points from the equation to plot the graph to the equation.