Question

How do you find the x and y intercept of \[2x+y=10\]?

Answer 1

Hint: In this problem we have to find the x-intercept and y-intercept of the given equation\[2x+y=10\]. We know that to find the point at x-intercept, the value of y is 0 and to find the point at y-intercept, the value of x is 0. By substituting the value of x = 0 in the given equation, we can get the y-intercept and by substituting the value of y = 0 in the given equation, we can get the x-intercept.

Complete step by step answer:
We know that the given linear equation is,
\[2x+y=10\] ……. (1)
We also know that at x-intercept, the value of y is 0 and at y-intercept the value of x is 0.
Now we can find the x-intercept, where y = 0.
Substituting the value of y in equation (1), we get
\[\begin{align}
  & \Rightarrow 2x+\left( 0 \right)=10 \\
 & \Rightarrow 2x=10 \\
 & \Rightarrow x=\dfrac{10}{2} \\
 & \Rightarrow x=5 \\
\end{align}\]
The x-intercept is \[\left( 5,0 \right)\].
Now we can find the y-intercept, where x = 0.
Substituting the value of x in equation (1), we get
\[\begin{align}
  & \Rightarrow 2\left( 0 \right)+y=10 \\
 & \Rightarrow y=10 \\
\end{align}\]
The y-intercept is \[\left( 0,10 \right)\]
Therefore, the x-intercept is \[\left( 5,0 \right)\] and the y-intercept is \[\left( 0,10 \right)\].

Note:
We should know that, in these types of problems, we can also use the slope-intercept formula to find the y-intercept and for x-intercept, the value of y is 0. We should always remember that at x-intercept, the value of y is 0 and at y-intercept, the value of x is 0.