Question

How do you find the slope given $y = \dfrac{3}{5}x + 5$?

Answer 1

We will first write the general equation of a line which is given by $y = mx + c$, where m is the slope of the line and then find the slope by comparing the given equation to the general equation.

Complete step by step answer:
We are given that we are required to find the slope of $y = \dfrac{3}{5}x + 5$.
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 $y = \dfrac{3}{5}x + 5$. If we compare this to the above mentioned line, we will then obtain: $m = \dfrac{3}{5}$ and c = 5.
Therefore, the slope of the given line is $\dfrac{3}{5}$.

Note:
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 $\dfrac{3}{5}$.
So, if we are required to find the angle the line is making with the positive direction of x – axis, then it would have been equal to ${\tan ^{ - 1}}\left( {\dfrac{3}{5}} \right)$.
The students must also note that this is the easiest way to find the slope of the line. We have an alternate way to do the same as well:-
Let us first find two points which lie on the given line.
Since, (0, 5) and (-5, 2) are the two points on the line $y = \dfrac{3}{5}x + 5$.
The slope of the line on which two points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ lie is given by the following expression:-
$\Rightarrow m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$, where m is the slope of the line.
Therefore, we will get the slope:-
$\Rightarrow m = \dfrac{{2 - 5}}{{ - 5 - 0}}$
Simplifying the right hand side of the above equation, we will then obtain the following expression with us:-
$\Rightarrow m = \dfrac{{ - 3}}{{ - 5}}$
Thus, we have the following required slope with us: $m = \dfrac{3}{5}$