Question

What is the y – intercept of the line with equation $ \dfrac{x}{3} - \dfrac{y}{2} = 1 $ ?

Answer 1

Hint: The given equation is in intercept form. The standard intercept form of a straight line is: $ \dfrac{x}{a} + \dfrac{y}{b} = 1 $ , where $ a = x - \operatorname{int} ercept $ and $ b = y - \operatorname{int} ercept $ . So, we need to arrange the given equation similar to the standard intercept form equation and then compare the given equation with standard form.

Complete step by step solution:
In this question, we are given an equation of straight line and we are supposed to find the value of y – intercept.
The given equation is:
 $ \Rightarrow \dfrac{x}{3} - \dfrac{y}{2} = 1 $ - - - - - (1)
Here, we can see that the given equation is in intercept form. Now, we can find the intercept of the given equation using two methods.
Using slope intercept form
Using intercept form
As we are given the intercept form already, we will be using the intercept form for finding the y – intercept.
The standard intercept form of a straight line is given by:
 $ \dfrac{x}{a} + \dfrac{y}{b} = 1 $
Where, $ a = $ x – intercept and $ b = $ y – intercept
So, we need to find the value of b.
Before that, we need to arrange the given equation in such a way that we can compare it with the standard equation.
Observe equation (1) closely, everything is the same as compared to the standard equation, only the difference is the negative sign. So, we need to change it.
 $ \Rightarrow \dfrac{x}{3} + \left( { - \dfrac{y}{2}} \right) = 1 $
Hence, now we can compare this equation with the standard equation.
On comparing, we get $ b = - 2 $ .
Hence, the y – intercept of the line with equation $ \dfrac{x}{3} - \dfrac{y}{2} = 1 $ is $ - 2 $ .
So, the correct answer is “-2”.

Note: The other method to find the value of y – intercept is by using slope intercept form. The slope intercept form is:
 $ y = mx + c $ , where m is the slope and c is the y – intercept.
So, arrange the given equation similar to the standard slope intercept form equation.
 $
   \Rightarrow \dfrac{x}{3} - \dfrac{y}{2} = 1 \\
   \Rightarrow \dfrac{{2x - 3y}}{6} = 1 \\
   \Rightarrow 2x - 3y = 6 \\
   \Rightarrow 3y = 2x - 6 \\
   \Rightarrow y = \dfrac{{2x - 6}}{3} \\
   \Rightarrow y = \left( {\dfrac{2}{3}} \right)x + \left( { - 2} \right) \;
  $
Hence, y – intercept $ = - 2 $