Question

How do you find the slope of $3x - y = 0$ ?

Answer 1

Hint: we can find the slope of the given equations by:
$1.$ Rewriting the given equations into the slope intercept form of the equation.
$2.$ Any equation written in the slope intercept form will directly give the term containing x as slope of the equation.

Complete step by step answer:
Let us start with the slope intercept form of equation:
But before proceeding to that we should be clear with the slope- intercept form of equation.
See, any equation which is given in the form $y = mx + c$ is the slope intercept form of the equation.
Now, we will start by writing the main equations that are given to us in the question:
$ \Rightarrow 3x - y = 0$
now, rewriting the above equation in slope- intercept form of equation:
It can be done by relocating all the terms that are not containing y to the RHS of the equation:
$ \Rightarrow - y = - 3x + 0$
Simplify by multiplying both side of the equation with minus sign:
$ \Rightarrow - ( - y) = - ( - 3x + 0)$
Simplify by cancelling the signs:
$ \Rightarrow \not{ - }(\not{ - }y) = - ( - 3x + 0)$
Simplify and rewrite the expression:
$ \Rightarrow y = 3x - 0$
As from the above equation we can now write the slope and y intercept as:
$ \Rightarrow y = 3x - 0$
Where, slope $m = 3$and $y$- intercept $c = - 0$.

Hence, we can say that the slope of the equation is $m = 3$ .

Note: It should be made clear that this is not the only way to find the slope of the equation. You can also solve it by adding or subtracting with the term containing x and constants to both the sides of the equation.
Like:
$ \Rightarrow 3x - y = 0$
Subtract with 3x on both the sides:
$ \Rightarrow 3x - y - 3x = - 3x + 0$
Simplify:
$ \Rightarrow - y = - 3x + 0$
Multiply both the sides with minus sign:
$ \Rightarrow - ( - y) = - ( - 3x + 0)$
Simplify:
$ \Rightarrow y = 3x - 0$
Here also the slope is $3$
Therefore, You will get the same result by doing it either way.