Question

How do you find the slope and y – intercept of $y = - 4x – 5$?

Answer 1

We will use the general equation of a line which is given by $y = mx + c$ and then find the slope by comparing and then we will put x zero in the given equation $y = - 4x – 5$ to find y intercept.

Complete step by step answer:
We are given that we are required to find the slope and the y - intercept of $y = - 4x – 5$.
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 $y = - 4x – 5$. If we compare this to the above mentioned line, we will then obtain: $m = - 4$ and $c = - 5$.
Therefore, the slope of the given line is – 4.
Now, we need to find the intercept. Let us put in x = 0 in the equation $y = - 4x – 5$ to find the y – intercept.
Putting x = 0 in $y = - 4x – 5$, we will get $y = - 5$.
So, the y – intercept of the given line is – 5.

Note: Here 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 slope of a line is basically the tangent of the angle the line makes with positive x – axis. Here, in this question, we have tangent of the angle the given line is making with positive x – axis as - 4.
If here, we would had to find the x – intercept, we would have just put y = 0 in the given equation $y = - 4x – 5$.