Question

How do you find the x and y intercepts for $y=-\dfrac{1}{2}x-4$ ?

Answer 1

Hint: In order to solve this question, we must have prior knowledge about intercepts of a straight-line and how they are represented in the equation of a line. We will find the x-intercept and y-intercept of the given equation of straight-line. Thus, we will first put $y=0$ and then we will put $x=0$ in the given equation to find the x-intercept and y-intercept respectively.

Complete step-by-step solution:
The x-intercept is the distance from origin of the point on the given function where the value of y is zero. This point logically lies on the x-axis and is given as $\left( a,0 \right)$ where $a$ is called the x-intercept.
The y-intercept is the distance from origin of the point on the given function where the value of x is zero. This point logically lies on the y-axis and is given as $\left( 0,b \right)$ where $b$ is called the y-intercept.
We are given the function, $y=-\dfrac{1}{2}x-4$.
In order to find the x-intercept, we will put $y=0$ and solve the equation accordingly. Hence, putting $y=0$, we get
$\Rightarrow \left( 0 \right)=-\dfrac{1}{2}x-4$
Taking -4 on the left-hand side, we get
$\Rightarrow 4=-\dfrac{1}{2}x$
Now, we will multiply the entire equation by -2.
$\begin{align}
  & \Rightarrow 4\left( -2 \right)=-\dfrac{1}{2}x\left( -2 \right) \\
 & \Rightarrow -8=x \\
\end{align}$
$\therefore x=-8$
Therefore, the x-intercept is equal to -8.
In order to find the y-intercept, we will put $x=0$ and solve the equation accordingly. Hence, putting $x=0$, we get
$\begin{align}
  & y=-\dfrac{1}{2}\left( 0 \right)-4 \\
 & \Rightarrow y=-4 \\
\end{align}$.
Therefore, the y-intercept is equal to -4.
Hence, the x and y intercepts for equation $y=-\dfrac{1}{2}x-4$ are $-8$ and $-4$ respectively.

Note: The equation of a straight line is expressed especially in an intercept form which is given as $\dfrac{x}{a}+\dfrac{y}{b}=1$ where $a$ is the x-intercept of line and $b$ is the y-intercept of the line as mentioned before. In this problem, $a=-8$ and $b=-4$. One essential feature of the intercept form of line is that its constant term is always equal to 1.