Question

How do you write the equation in point slope form given $x$ -intercept of $-4$ and a $y$ -intercept of $-1$?

Answer 1

Hint: There are many equations of a line. But at the end, all the different equations or the different forms of line talk about the same line. Now, let us specifically look at the intercept form of a line. Intercepts of a line are made when a line cuts both the axes. The length that the lines cut on both the axes is the intercept of the particular axis. The general equation of a intercept form is $\dfrac{x}{a}+\dfrac{y}{b}=1$ where $a$ is the length of intercept formed on the $x$ axis and $b$ is length of the intercept formed on the $y$ axis.

Complete step by step solution:
So in the question we are given that $-4$ is the intercept. So it means that it is the length of the $x$ intercept. And $-1$ is the $y$ intercept. It means that it is the length of the $y$ intercept.
So the general equation of the an intercept form of the line is $\dfrac{x}{a}+\dfrac{y}{b}=1$.
Upon comparing , we can conclude that $a=-4$ as $a$ indicates the length of intercept formed by the line on $x$-axis. And $b=-1$ as $b$ represents the length of the intercept by the line on $y$-axis.
Now let us build the equation.
$\begin{align}
  & \dfrac{x}{a}+\dfrac{y}{b}=1 \\
 & \dfrac{x}{-4}+\dfrac{y}{-1}=1 \\
 & \dfrac{x}{4}+\dfrac{y}{1}=-1 \\
\end{align}$
$\therefore $ Hence, the slope equation of a line with the given intercepts is $\dfrac{x}{4}+\dfrac{y}{1}=-1$.
Graph for reference :

Note: We should be well aware of all the general equations of all the forms of line so as to complete the questions quickly. We have to be careful while comparing as one simple mistake can completely change the equation of a line and change the way it looks on a graph.