Question

What is the slope and intercept of $y=-4x-6$ ?

Answer 1

From the question given that we have to find the slope and intercept of $y=-4x-6$. 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 $y=-4x-6$ to find the intercept.

Complete step-by-step answer:
We are given that we are required to find the slope and the y-intercept of
$\Rightarrow y=-4x-6$
The general equation of a line is given by
$\Rightarrow y=mx+c$
where m is the slope of the line.
Now, we are given the line $y=-4x-6$. If we compare this to the above-mentioned line, we will then obtain
$\Rightarrow m=-4$
And
$\Rightarrow c=-6$
Therefore, the slope of the given line is $-4$.
Now, we need to find the intercept. Let us put $x=0$ in the equation $y=-4x-6$ to find the y-intercept.
Putting $x=0$ in $y=-4x-6$ we will get
$\Rightarrow y=-4\left( 0 \right)-6$
$\Rightarrow y=-6$
So, the y-intercept of the given line is $-6$.

Note: Here x and y intercepts basically refer to the points where the line cuts the x-axis and y axis. The point where Coordinate axis cuts 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 -axis. Here, in this question we have the tangent of the angle the given line is making with positive X-axis is -4. If we had to find the X- intercept, we would have just put y=0 in the given equation $y=-4x-6$, that is x-intercept is $x=\dfrac{-3}{2}$.