Question

Given $y = - 4x + 3$ how do you find the slope?

Answer 1

First of all we will be doing is to find the value of m from the given equation $y = - 4x + 3$. To do that we will compare with the general equation $y = mx + c$. This step will give us that, m=-4 in the given question. Now, we know that slope is the tangent of the value of m. Therefore we will find the tangent of -4 which will be $\theta = {\tan ^{ - 1}}4$. Hence, we can conclude that, $\theta = {\tan ^{ - 1}}4$ is the slope of the given equation $y = - 4x + 3$.

Complete step by step answer:
We know that a slope of a line is the gradient of that line. In easy words, it’s the angle by which it is inclined with the x axis. But the point to remember is that, the value is in tangent.
$slope = \tan \theta$
Now, we know that for a line with a general equation $y = mx + c$. m is the value of slope.So, if we compare both the equations we can conclude that, in the given question:-
$y = y$
$\Rightarrow m = - 4$
$\Rightarrow c = 3$
Hence, value of slope is $m = - 4$
So,
$m = - 4 = \tan \theta \\\ \Rightarrow \tan \theta = - 4 \\\ \therefore\theta = {\tan ^{ - 1}}4 \\\$
Therefore, we can conclude that the slope of the given equation is $\theta = {\tan ^{ - 1}}4$.

Note: In order to find the angle, that is the slope of the equation, you must equate the value of m to tan and get the answer. Just writing m=-4 as the slope won’t complete the answer as we just discussed slope is the tangent of the angle and not just the value itself.Leaving the question at the initial part will give wrong answers.