Question

How do you find the slope and intercept of y = x – 10?

Answer 1

We will first write the general equation of a line and then find the slope by comparing and then we will put x and y zero in the given equation to find y and x intercepts respectively.

Complete step-by-step answer:
We are given that we are required to find the slope and intercept of y = x – 10.
The general equation of a line is given by y = mx + c, where m is the slope of the line.
Now, we are given the line y = x - 10. If we compare this to the above mentioned line, we will then obtain: m = 1 and c = - 10.
Therefore, the slope of the given line is 1.
Now, we need to find the intercepts. Let us first put in x = 0 in the equation y = x - 10 to find the y – intercept.
Putting x = 0 in y = x - 10, we will get y = - 10.
So, the y – intercept of the given line is – 10.
Let us now put in y = 0 in the equation y = x - 10 to find the x – intercept.
Putting y = 0 in y = x - 10, we will get x – 10 = 0
Taking the 10 from this side to other side, we will get: x = 10

So, the x – intercept of the given line is 10.

Note:
The students must note that the x and y intercepts basically refer to the points where the line cuts the x – axis and y – axis at. The point where coordinate axis cut the line at x – axis is x – intercept and y – axis is y – intercept.
The students must also know that the slope of a line is basically the tangent of the angle the line makes with the positive x – axis. Here, in this question, we have tangent of the angle the given line is making with the positive x – axis as 1.