Question

How do you find the slope and intercept of $y = - 8x - 7$?

Answer 1

We will first write 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 given equation $y = - 8x - 7$ to find $y$ - intercept and then $y = 0$ to find the $x$ – intercept.

Complete step by step solution:
We are given that we are required to find the slope and the intercept of $y = - 8x - 7$.
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 $y = - 8x - 7$. If we compare this to the above mentioned line, we will then obtain: $m = - 8$ and $c = - 7$.
Therefore, the slope of the given line is - 8.
Now, we need to find the intercepts of the line $y = - 8x - 7$.
Let us put in $x = 0$ in the equation $y = - 8x - 7$ to find the $y$ – intercept.
Putting $x = 0$ in $y = - 8x - 7$, we will then get $y = - 7$.
So, the $y$ – intercept of the given line is – 7.
Let us put in $y = 0$ in the equation $y = - 8x - 7$ to find the $x$ – intercept.
Putting $y = 0$ in $y = - 8x - 7$, we will then get $7 = - 8x$.
Dividing by – 8, we will then obtain the following:-
$\Rightarrow x = - \dfrac{7}{8}$
So, the $x$ – intercept of the given line is $- \dfrac{7}{8}$.
Thus, we have the final answer as follows:-
The slope of the given line $y = - 8x - 7$ is - 8.

The $x$ - intercept and the $y$ – intercept of the given line $y = - 8x - 7$ is - 7 and $- \dfrac{7}{8}$ respectively.

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 the 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 is - 8.