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 $$x$$
$$\Rightarrow x={\displaystyle \frac{3}{2}}$$
$$\Rightarrow x=1.5$$
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.