Question

How do you find the slope of x – y = 5?

Answer 1

Hint: We will first write the general equation of a line and then compare it to the given equation and thus we have the slope and our answer.

Complete step-by-step answer:
Let us first write the general equation of the line.
The general equation of a line is given by y = mx + c, where m gives the slope of the line.
Now, we are given the line x – y = 5.
Now, we will just take x from addition in the left hand side to subtraction in right hand side to get the following equation:-
$ \Rightarrow $- y = 5 – x
Now, let us multiply the whole equation by – 1 to get the following equation:-
$ \Rightarrow $ y = - ( 5 – x )
Now, if we open the bracket to get the equation given by the following expression:-
$ \Rightarrow $ y = - 5 + x
We can now right the above equation as the following expression:-
$ \Rightarrow $ y = x – 5
Now, if we compare it to the given equation : y = mx + c.
We will then obtain the following terms: m = 1 and c = - 5.

Hence, the slope of the equation is 1.

Note:
The students must note that the slope of the line means the tangent of the angle which the line makes with the positive x – axis. The slope of a line gives us the knowledge about the inclination of the line with the co – ordinate axis. We can also find the slope of a line using two points through which our line passes.
The students must note that the c in the equation y = mx + c represents the intercept of the line given.