Question

How do you find the slope given $y = - 5x + 3$?

Answer 1

Hint: In this question, we need to find the slope of the given straight line. We know that the general equation of a straight line in slope intercept form is given by $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. Comparing the given equation with the general equation of a straight line we can determine the slope of the required line and obtain the result as wanted.

Complete step by step solution:
Given the equation $y = - 5x + 3$ …(1)
Note that the above expression given in the equation (1) is an equation of a straight line.
Here we are asked to find out the slope of the given line.
Firstly, let us define a general equation of a straight line.
The general equation of a straight line in slope intercept form is given by,
$y = mx + c$ …… (2)
where $m$ is the slope of the straight line, $c$ is the y-intercept.
Note that the y-intercept $c$ is always a constant.
Now let us proceed further.
We now convert the given equation of a straight line into general form.
If we observe carefully, the given equation of a straight line directly matches with the general equation. So there is no need to convert or make any rearrangement in the given equation.
Consider the given equation $y = - 5x + 3$.
Comparing with the general slope intercept form given in the equation (2), we get,
$ \Rightarrow m = - 5$ and $c = 3$
Which is the slope and y-intercept of the given straight line.

Hence we can conclude that the slope of the straight line $y = - 5x + 3$ is $m = - 5$.

Note :
In this question, it is important to remember that $y = mx + c$ is the form called the slope intercept form of the equation of the straight line. It is the most popular form of the straight line.
Sometimes the given equation of a line won’t be the same as the general form. We need to convert or make rearrangement in the given expression such that it becomes similar to the general slope intercept form. So then, it becomes easier to find the required things.