Question

How do you graph $y = - 6 + 2x$ using the intercepts?

Answer 1

Hint : As we can see that we have an equation and it is a linear equation in two variables. We need to plot a graph for the given equation, For plotting a graph we need different $x$ value as well as $y$ value. So we need to find the values by substituting $y = 0$ and $x = 0$ respectively, after these we need to plot these on the graph.

Complete step by step solution:
According to the question we have the equation $y = - 6 + 2x$ .
We will first determine the $x$ intercept by putting $y = 0$ , So we have $0 = 2x - 6$ .
By adding both the sides by $6$ we have,
$0 + 6 = 2x - 6 + 6 \Rightarrow 6 = 2x$ , So we have the value of $x = \dfrac{6}{2} = 3$ .
So we have the $x$ intercept $(x,y) = (3,0)$ .
Now we will determine the $y -$ intercept, this time we substitute the value $= 0$ , so we have $y = 2(0) - 6 \Rightarrow y = - 6$ . Hence the $y -$ intercept is $(x,y) = (0, - 6)$ .
Now we will put them into graph:

Hence in the above figure we have point A $(3,0)$ and point B $(0, - 6)$ .

Note : Before solving this kind of question we should be aware of the $x$ and $y$ axis and how to plot their values. The calculations should be done carefully to avoid calculation mistakes because it will create a wrong graph. We should note that the above equation is a linear equation so the graph is always a straight line.