Question

How do you graph $y = 4 - 3x?$

Answer 1

Hint: First find a few random points from which the given line is passing by putting random values of the independent variable (x) in the given equation, to get the values of the dependent variable (y). Go for smaller values like $0,\;1,\;2,$ etc, larger values will make the graph a bit complicated to take its scale and in plotting it. And when plotting the graph, take the scale in between $1\;{\text{to}}\;5$, don’t take large scales.

Complete step by step solution:
In order to graph the equation $y = 4 - 3x$, firstly we have to find some values of $x\;{\text{and}}\;y$, we will put some values of $x$ in the equation and then get respective values of $y$
For this we will create a table in which we will write the values of $x,\;y$ and the coordinates of points we will get, creating the table below.

Random values of $x$	Value of $y = 4 - 3x$	Coordinates(x, y)
$0$	$y = 4 - 3 \times 0 = 4 - 0 = 4$	$(0,\;4)$
$1$	$y = 4 - 3 \times 1 = 4 - 3 = 1$	$(1,\;1)$
$ - 1$	$y = 4 - 3 \times ( - 1) = 4 + 3 = 7$	$( - 1,\;7)$
$2$	$y = 4 - 3 \times 2 = 4 - 6 = - 2$	$(2,\; - 2)$

Now, you can see in the table, how we have calculated the value of $y$ by putting random values of $x$ in the above equation. Now, we have the three co-ordinates of the required graph, i.e.$(0,\;4),\;(1,\;1),\;( - 1,\;7)\;{\text{and}}\;(2,\; - 2)$. So, we will now plot these three points on the graph as follows

So, we have plotted all the points on the graph, now we have to draw a line passing through these points to get the required graph of the equation, we will get

This is the required graph of the equation $y = 4 - 3x$

Note: When finding the passing points of the line find points which have reasonable distance to each other so that taking the scale of the graph will become easy. You can plot the graph directly by finding its intercepts.