Question

How do you graph $ 3x-y=3 $ using intercepts?

Answer 1

Hint: In the problem, they have asked to draw the graph of the line $ 3x-y=3 $ using intercepts. We know that the intercepts are the points where the line meets the $ x-axis $, $ y-axis $ . We know that the equation of the $ x-axis $ is $ y=0 $ . So, we will substitute $ y=0 $ in the given equation to calculate the point where the line meets the $ x-axis $. We know that the equation of the $ y-axis $ is $ x=0 $ , so we will substitute $ x=0 $ in the given equation to calculate the point where the given line meets the $ y-axis $ . Now we will denote these points on graph paper and join them together to get the required graph.

Complete step by step answer:
Given that, $ 3x-y=3 $ .
Finding the point where the line meets the $ x-axis $ by substituting $ y=0 $ in the above equation, then we will get
 $ \begin{align}
  & 3x-0=3 \\
 & \Rightarrow 3x=3 \\
\end{align} $
Dividing the above equation with $ 3 $ on both sides, then we will get
 $ \begin{align}
  & \Rightarrow \dfrac{3x}{3}=\dfrac{3}{3} \\
 & \Rightarrow x=1 \\
\end{align} $
Hence the line $ 3x-y=3 $ meets the $ x-axis $ at point $ \left( 1,0 \right) $ .
Finding the point where the line meets the $ y-axis $ by substituting $ x=0 $ in the above equation, then we will get
 $ \begin{align}
  & 3\left( 0 \right)-y=3 \\
 & \Rightarrow -y=3 \\
\end{align} $
Multiplying negative sign on both sides, then we will get
 $ \begin{align}
  & \Rightarrow -\left( -y \right)=-3 \\
 & \Rightarrow y=-3 \\
\end{align} $
Hence the line $ 3x-y=3 $ meets the $ y-axis $ at point $ \left( 0,-3 \right) $ .
Now plotting the points $ \left( 1,0 \right) $ , $ \left( 0,-3 \right) $ on a graph paper and joining them to get the graph of the given line. Then the graph looks like below

Note: In the problem, they have mentioned that plot the graph using intercepts so we have calculated the intercepts of the line. If they don’t mention the intercepts, they can use the standard form where we will calculate the value of one variable by taking the values of another variable in a certain range.