Question

How do you find the x and y-intercept of $4x+y=5$?

Answer 1

Hint: We need to find the value of x and y-intercepts, for that, we use the Substitution Method. An intercept is a point on the x-axis or y-axis through which the slope of the line passes. This implies that for the y-intercept, the y-coordinate of a point lies on the line or the curve and which passes through the y-axis, similarly for the x-intercept. For finding the x-intercept, we simply put the value y=0 in the equation and solve for x. Similarly for the y-intercept, we put x=0 in the equation and step by step solve for y.

Complete step by step answer:
According to the question, we have to find the value of x-intercept and y-intercept.
So, it is given that the equation is: \[4x+y=5\] --- (1)
Thus, by implying the Substitution method in the coordinates, that is
For x-intercept:
Let the coordinate be \[A\left( x,y \right)\] .
So to find x-coordinate, let us substitute\[y=0\] in equation (1),
Thus x-intercept \[A\left( x,y \right)\] will become$A(x,0)$, we get
\[\begin{align}
  & \Rightarrow 4x+0=5 \\
 & \Rightarrow 4x=5 \\
\end{align}\]
Now, on dividing both the sides by 4, we get
$\begin{align}
  & \Rightarrow \dfrac{4x}{4}=\dfrac{5}{4} \\
 & \Rightarrow x=\dfrac{5}{4} \\
 & \Rightarrow x=1.25 \\
\end{align}$
\[\therefore \text{ we get x-intercept as }A(1.25,0)\]
Similarly, for y-intercept:
Let the coordinate as\[B(x,y)\] .
So for y-coordinate, let \[x=0\]in equation (1),
Thus y-intercept \[B(x,y)\] will become$B(0,y)$ , we get
\[\begin{align}
  & \Rightarrow 4(0)+y=5 \\
 & \Rightarrow 0+y=5 \\
 & \Rightarrow y=5 \\
\end{align}\]
\[\therefore \text{ we get y-intercept as }B(0,5)\]
Graph for the equation $4x+y=5$ with x-intercept A (1.25, 0) and y-intercept B (0, 5) is,

Thus, we get the value of x-intercept is \[A\left( x,0 \right)=A\left( 1.25,0 \right)\] and, the value of y-intercept is \[B(0,y)=B(0,5)\] for the equation $4x+y=5$.

Note:
For such types of questions, you should always keep in mind that for x-intercept, always substitute y=0 in the equation instead of x=0, similarly, for y-intercept, put x=0 in the equation and not y=0, which implies that always substitute the value of the coordinates correctly for finding the intercepts. We can also find the x-intercept and y-intercept using a simpler method, that is by comparing the given equation with $\dfrac{x}{a}+\dfrac{y}{b}=1$ and get the intercepts as (a, 0) and (0, b).