Question

Determine the graph of the equation \[y = 2x - 3\] ?

Answer 1

Hint: 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.