Question

What is the ‘y’ intercept of \[x-y=12\]?

Answer 1

Hint: We are given a question in which we are given the equation of a line. We are asked to find the y – intercept of the given equation of the line. In order to find the y – intercept of the given line, we will modify the equation to look like the slope intercept for which is, \[y=mx+c\]. After the modification, we will have the equation as, \[y=x-12\]. We will then compare the slope intercept form equations and the corresponding value of ‘c’ is our required y – intercept for the given equation of the line.

Complete step-by-step answer:
According to the given question, we are given the equation of a line and we are asked to find the y – intercept of the given equation.
The equation that we have is,
\[x-y=12\]
We will first write this given equation in the slope intercept form, which is, \[y=mx+c\]. Here, ‘m’ is the slope of the given equation and ‘c’ is the y – intercept. After having the required equation, then we can begin to find the required intercept of y coordinate.
We will now subtract ‘x’ on both the sides of the given equation, we get,
\[\Rightarrow -y=-x+12\]
We will now take negative signs on both the sides of the inequality and we have,
\[\Rightarrow y=x-12\]
On comparing the above equation with the expression of slope intercept form, we get the value of ‘c’ the y – intercept as,
\[c=-12\]
Therefore, the y – intercept of the given equation is \[-12\].

Note: The above question can also be solved by making use of the idea that at y – intercept, we have the coordinate of that point as \[\left( 0,c \right)\], that is, the x – coordinate is 0 at that point. So, we can substitute the value of the ‘x’ as 0 in the given equation and we will get the value of the y – intercept.
The given equation that we have is,
\[x-y=12\]
Substituting the value of \[x=0\], we get,
\[0-y=12\]
We get the value of ‘y’ as,
\[\Rightarrow -y=12\]
\[\Rightarrow y=-12\]
Therefore, the y – intercept of the given equation is \[-12\].