Question

How do you find the slope and intercept of $y = - \dfrac{2}{3}x - 1$?

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 $y = - \dfrac{2}{3}x - 1$.
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 $y = - \dfrac{2}{3}x - 1$. If we compare this to the above mentioned line, we will then obtain: $m = - \dfrac{2}{3}$ and c = - 1.
Therefore, the slope of the given line is $- \dfrac{2}{3}$.
Now, we need to find the intercepts. Let us first put in x = 0 in the equation $y = - \dfrac{2}{3}x - 1$ to find the y – intercept.
Putting x = 0 in $y = - \dfrac{2}{3}x - 1$, we will get y = -1.
So, the y – intercept of the given line is – 1.
Let us now put in y = 0 in the equation $y = - \dfrac{2}{3}x - 1$ to find the x – intercept.
Putting y = 0 in $y = - \dfrac{2}{3}x - 1$, we will get $- \dfrac{2}{3}x - 1 = 0$
Taking the 1 from this side to other side, we will get: $- \dfrac{2}{3}x = 1$

So, the x – intercept of the given line is $- \dfrac{3}{2}$.

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 $- \dfrac{2}{3}$.