Question

What is the standard form of the equation of a line with x - intercept 2 and y - intercept $ - 6 $ ?

Answer 1

Hint: We are given the values of x – intercept and y – intercept. First of all, write the intercept form of the equation that is $ \dfrac{x}{a} + \dfrac{y}{b} = 1 $ . Then simplify the equation and obtain the equation in form of a standard line equation that is $ ax + by = c $ .

Complete step by step solution:
In this question, we are given the values of x – intercept and y – intercept and we are supposed to find the standard form of the equation.
Now, the standard form of equation of line is: $ ax + by = c $ - - - - - - - (1)
So, we have to obtain the equation in the form of the above given equation.
Now, the intercept form equation is given by: $ \dfrac{x}{a} + \dfrac{y}{b} = 1 $ ,
Where, $ a = $ x – intercept and $ b = $ y – intercept.
Therefore, according to our question,
 $ \Rightarrow \dfrac{x}{2} + \dfrac{y}{{ - 6}} = 1 $ - - - - - - - (2)
Taking L.CM. Equation (2) becomes,
 $
   \Rightarrow \dfrac{{3x - y}}{6} = 1 \\
   \Rightarrow 3x - y = 6 \;
  $
This is our required answer. This is the standard form of the equation.
Comparing our answer with equation (1), we get
 $ a = 3,b = - 1,c = 6 $
So, the correct answer is “3x - y = 6”.

Note: One of the other important forms of straight lines is the slope intercept form. It is represented by
 $ y = mx + b $ , where m is the slope of the line and b is the y – intercept. It is known as slope intercept because m represents the slope of line and b represents the y – intercept of the line.