Question

How do you graph $y=4x+3$ using a table?

Answer 1

Hint: To draw the graph of the above equation $y=4x+3$, we are going to plot the points which have x and y coordinates. Take the integral value of x from -2 to +2 and then substitute these points of x and see what coordinates of y, we are getting. Then plot these points on the graph paper.

Complete step by step answer:
The equation given above is a straight line equation and the equation is as follows:
$y=4x+3$
Now, we are going to take the integral values of x from -2 to +2 and then see what values of y we are getting.
Substituting x as -2 in the above equation we get,
$\begin{align}
  & y=4\left( -2 \right)+3 \\
 & \Rightarrow y=-8+3=-5 \\
\end{align}$
From the above, the first point we got as (-2, 5).
Substituting x as -1 in the above equation we get,
$\begin{align}
  & y=4\left( -1 \right)+3 \\
 & \Rightarrow y=-4+3=-1 \\
\end{align}$
From the above, second point we got as (-1, -1)
Substituting x as 0 in the above equation we get,
$\begin{align}
  & y=4\left( 0 \right)+3 \\
 & \Rightarrow y=0+3=3 \\
\end{align}$
From the above, third point we got as (0, 3).
Substituting x as 1 in the above equation we get,
$\begin{align}
  & y=4\left( 1 \right)+3 \\
 & \Rightarrow y=4+3=7 \\
\end{align}$
From the above, fourth point we got as (1, 7).
Substituting x as 2 in the above equation we get,
$\begin{align}
  & y=4\left( 2 \right)+3 \\
 & \Rightarrow y=8+3=11 \\
\end{align}$
From the above, fifth point we got as (2, 11).
From the above, we have tabulated the points that we solved above as follows:

x	-2	-1	0	1	2
y	-5	-1	3	7	11

Now, we are going to plot these points on the graph paper as follows:

In the above, we have marked the points by A, B, C, D and E. Now, we will join these points to make a straight line.

Hence, we have drawn the equation $y=4x+3$ on the graph paper.

Note:
You can check the equation of straight line that we drew is correct or not by marking the y coordinate as 6 and on the straight line then to find the x coordinate corresponding to 6 we are going to drop a perpendicular on the x axis from the point on the line and then see at what x values, y is 6.

In the above graph, as you can see that point F is the point whose y coordinate is 6 which we have shown by point K and the x coordinate that you can see is the intersection of the perpendicular from point F on the x axis and the point is G and the x coordinate of G is $\dfrac{3}{4}$.
This x coordinate you can see by zooming into point G.
 

Now, substituting the value of y as 6 in the above equation and we get,
$\begin{align}
  & 6=4x+3 \\
 & \Rightarrow 6-3=4x \\
 & \Rightarrow 3=4x \\
 & \Rightarrow x=\dfrac{3}{4}=0.75 \\
\end{align}$
As you can see that we are getting the same value of x which we got from the graph.
Hence, this means that the graph which we drew above is correct.