Question

What is the \[x\] and \[y\] intercept for \[x-2y=8\]?

Answer 1

Hint: The \[x\] and \[y\] intercepts can be found by using the point- slope formula of a line. The\[x\] intercepts can be found by substituting suitable values such that it satisfies the condition \[y=0\]. In the same way, \[y\] intercepts can be found by evaluating the given function for \[x=0\].

Complete step by step solution:
Now let us know more about the point-slope formula as we are going to apply it in our problem.
Point-slope form: It is the general form for the linear equations. It emphasizes the slope of the line and a point on the line which is not the \[y\] intercept. The general form of the point-slope form is \[y=mx+b\] where \[m\] denotes the slope and \[b\] denotes the \[y\] intercept.
Now let us proceed with the line equation given to us \[x-2y=8\].
On comparing it with the general form of the point-slope formula, we have to rearrange the given equation.
On rearranging we get,
\[-2y=-x+8\]
On evaluating for the \[y\] value, we get
\[y=\dfrac{1}{2}x-4\]
In order to find the \[x\] intercept, we have
\[y=\dfrac{1}{2}x-4=0\]
On solving, we get
\[\begin{align}
  & \dfrac{1}{2}x=4 \\
 & x=8 \\
\end{align}\]
\[\therefore \] The \[x\] intercept is \[\left( 8,0 \right)\]
To find out the \[y\] intercept, we have to substitute \[x=0\] into the equation.
\[\begin{align}
  & y=\dfrac{1}{2}x-4 \\
 & =\dfrac{1}{2}\left( 0 \right)-4 \\
 & =0-4 \\
 & =-4 \\
\end{align}\]
\[\therefore \] The \[y\] intercept will be \[\left( 0,-4 \right)\]

Note: \[y=mx+b\] is another form of the equation of point-slope form i.e. \[\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)\]. The \[b\] in the equation \[y=mx+b\] is where the line crosses the \[y-axis\]. If we want to find out the slope-point equation, when the slope values and intercepts are given, we must be using \[\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)\] to find the equation. When the graph is plotted the line passes through \[\left( 8,0 \right) and \left( 0,-4 \right)\]
Now let us plot the line equation we have \[x-2y=8\].