Question

How do you find the slope of $y = - \dfrac{5}{2}x - 5?$

Answer 1

Hint: To find the slope of the given equation, find the derivative of the given equation with respect to $x$, because slope is also known as the change in “y” with change in “x”.

Complete step by step solution:
In order to find the slope of the line $y = - \dfrac{5}{2}x - 5$, we will find its derivative with respect to $x$ as follows
$ \Rightarrow y = - \dfrac{5}{2}x - 5$
Differentiating both sides of the equation, with respect to $x$, we will get
$
   \Rightarrow \dfrac{{dy}}{{dx}} = \dfrac{{d\left( { - \dfrac{5}{2}x - 5} \right)}}{{dx}} \\
   \Rightarrow \dfrac{{dy}}{{dx}} = - \dfrac{5}{2} \\
 $
Therefore $ - \dfrac{5}{2}$ is the required slope of the given straight line equation.

Additional information:
There are two more methods to find out the slope of the given straight line equation, first one is express the given straight line equation in slope intercept form of straight line which is given as $y = mx + c$ where $m\,{\text{and}}\;c$ are slope of the straight line and its y-intercept respectively. And after expressing it in slope intercept form, compare it to the standard equation of slope intercept form to get the required value of slope. Second one is the method derived from the definition of slope that is slope is the changes in “y” with change in “x”, in this method find any two points from which the line is passing and then slope will be given as ratio of difference between their y-coordinates to x-coordinates. These two methods are only suitable for the equation of a straight line whereas the differentiation method holds good for all types of equations.

Note: When differentiating, take care of the fact that you are differentiating each and every term of the equation either variable or constant. Also the derivative of any constant is zero irrespective of the irrespective of the base by which you are differentiating.