Question

How do you write the standard form of a line given x intercept= -5, y intercept =-5?

Answer 1

This question is from the topic of straight line. In solving this question, we will first understand what the equation of general form of straight line is. From there, we will get to know about the x-intercept and y-intercept. After that, we will use the given intercepts and find the standard form of line. After that, we will get our answer.

Complete step-by-step solution:
Let us solve this question.
In this question, we have to find the stand form of straight line using the given data. It is given that x-intercept of line is -5 and y-intercept of line is -5.
Let us first understand the equation for general form of straight line.
The general form of straight line is:
$ax+by=c$
Where, y-intercept = $\dfrac{c}{b}$
And, x-intercept = $\dfrac{c}{a}$
The equation $ax+by=c$ can also be written as
$\dfrac{a}{c}x+\dfrac{b}{c}y=1$
The above equation can also be written as
$\Rightarrow \dfrac{x}{\dfrac{c}{a}}+\dfrac{y}{\dfrac{c}{b}}=1$
So, it is given in the question that x-intercept (that is $\dfrac{c}{a}$) is -5 and x-intercept (that is $\dfrac{c}{b}$) is -5.
Therefore, after putting the values, we can write the equation $\dfrac{x}{\dfrac{c}{a}}+\dfrac{y}{\dfrac{c}{b}}=1$ as
$\Rightarrow \dfrac{x}{-5}+\dfrac{y}{-5}=1$
Now, we will multiply -5 to both the side of the equation, we can write
$\Rightarrow \left( -5 \right)\times \left( \dfrac{x}{-5}+\dfrac{y}{-5} \right)=\left( -5 \right)\times 1$
The above equation can also be written as
$\Rightarrow \left( -5 \right)\times \dfrac{x}{-5}+\left( -5 \right)\times \dfrac{y}{-5}=-5$
The above equation can also be written as
$\Rightarrow x+y=-5$
Hence, we get that the equation of line is $x+y=-5$ whose x intercept is -5 and y intercept is -5.

Note: We should have a better knowledge in the topic of straight line to solve this type of question. We should know about the equation for the general form of straight line. The equation for general form of straight line is in the following:
$ax+by=c$
Where, x-intercept is $\dfrac{c}{a}$
And, y-intercept is $\dfrac{c}{b}$