Question

What is the $x$ and $y$ intercept for $x-2y=8$?

Answer 1

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

& \dfrac{1}{2}x=4 \\\ & x=8 \\\ \end{aligned}$$ $$\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{aligned} & y=\dfrac{1}{2}x-4 \\\ & =\dfrac{1}{2}\left( 0 \right)-4 \\\ & =0-4 \\\ & =-4 \\\ \end{aligned}$$ **$$\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$$.