Question

How do you find x and y intercept and write each as an ordered pair for the following straight line $-3x+4y=8$ ?

Answer 1

Hint: The straight line equation given in the above problem of which we have to find the x and y intercept is as follows: $-3x+4y=8$. Now, to find the x intercept, we will put y as 0 in the given equation and then the value of x corresponding to such y is the x intercept. The y intercept is calculated by putting x as 0 in the given equation and then the y corresponding to such x is the y intercept.

Complete step by step answer:
The equation of a straight line given in the above problem is as follows:
$-3x+4y=8$
Now, we are going to find the x intercept of the above equation by putting y as 0 in the above equation and we get,
$\begin{align}
  & \Rightarrow -3x+4\left( 0 \right)=8 \\
 & \Rightarrow -3x=8 \\
\end{align}$
Dividing -3 on both the sides we get,
$\begin{align}
  & \Rightarrow \dfrac{-3x}{3}=\dfrac{8}{3} \\
 & \Rightarrow -x=\dfrac{8}{3} \\
\end{align}$
Multiplying -1 on both the sides in the above equation we get,
$x=-\dfrac{8}{3}$
Hence, the x intercept in the above equation is equal to $-\dfrac{8}{3}$ and the ordered pair corresponding to this x intercept is $\left( -\dfrac{8}{3},0 \right)$.
Now, the y intercept of the straight line is calculated by putting x as 0 in the above equation of straight line we get,
$\begin{align}
  & \Rightarrow -3\left( 0 \right)+4y=8 \\
 & \Rightarrow 0+4y=8 \\
\end{align}$
Dividing 4 on both the sides of the above equation and we get,
$\begin{align}
  & \Rightarrow \dfrac{4y}{4}=\dfrac{8}{4} \\
 & \Rightarrow y=2 \\
\end{align}$
Hence, the y intercept of the above straight line is equal to 2 and the ordered pair corresponding to the y intercept is $\left( 0,2 \right)$.

Note: The x and y intercept of the straight line is the point from the origin by a straight line on the x and y axis respectively. Meaning x intercept is the point on the x axis from where the line is cutting the x axis and y intercept is a point on the y axis at which the straight line is cutting y axis.