Question

Determine the graph of the equation $y = 2x - 3$ ?

Answer 1

To determine the graph we need different $x$ values as well as their corresponding values of $y$. To solve this question, we take any value of $x$ and then find the corresponding value of $y$ and vice versa. In this way, we find two points and plot them on the graph and join them in order to get the graph of the equation.

Complete answer:
Given equation is $y = 2x - 3$
To plot a graph of the given equation $y = 2x - 3$, we need points.
To find the first point let us put $x = 0$ and find the corresponding value of $y$.
On putting the value $x = 0$ in the given equation.
$y = 2 \times 0 - 3$
On simplifying we get the value of $y$
$\Rightarrow y = - 3$
This means when $x=0$, the value of $y$ on the graph is $-3$. On observing the values of $x$ and $y$ we get the first point.
$A$ be the first point. $A = \left( {0, - 3} \right)$
To find the second point we put $y = 0$ and find the corresponding value of $x$.
On putting the value $y = 0$ in the given equation.
$0 = 2 \times x - 3$
On taking 3 to another side
$2 \times x = 3$
On simplifying we get the value of $x$
$\Rightarrow x = \dfrac{3}{2}$
$\Rightarrow x = 1.5$
On observing the values of $x$ and $y$ we get the second point.
$B$ be the first point. $B = \left( {1.5,0} \right)$
Now we make a table of these points.

$x$	$y$
0	-3
1.5	0

Now we put these points in the graph and join them to obtain the graph of the equation.
On putting these points in the graph. The graph looks like-

Note:
To plot the graph of the linear equation we need a minimum of two points but we are unable to make a line with a single point. More points are required if we make a curve then more points are required and with more points, our curve is more accurate.