Question

How do you find the slope of the line $4x - 3y + 7 = 0$?

Answer 1

The slope of a line is a number that measures its steepness, usually denoted by the letter $m$.
Also we know that:
Slope intercept form of the line: $y = mx + c$ where $m$ is the slope of the line. Such that using the above equation we can find the slope of the given line.

Complete step by step solution:
Given
$4x - 3y + 7 = 0...............................\left( i \right)$
Now we have to find the slope of the line passing through the given points.
So for finding the slope of a line we have the equation:
Slope intercept form of the line: $y = mx + c.............................\left( {ii} \right)$
Where m is the slope of the line.
So we have to convert the equation (i) into (ii) and thus find the value of $m$.
So let’s divide the equation (i) with 3 such that we get:
$4x - 3y + 7 = 0 \\\ \dfrac{4}{3}x - \dfrac{3}{3}y + \dfrac{7}{3} = 0 \\\ \dfrac{4}{3}x - y + \dfrac{7}{3} = 0.........................\left( {iii} \right) \\\$
Rearranging (iii):
$y = \dfrac{4}{3}x + \dfrac{7}{3}........................\left( {iv} \right)$
Now on comparing (iv) and (ii) we can write:
$m = \dfrac{4}{3}$

Therefore the slope of the line $4x - 3y + 7 = 0$ is $\dfrac{4}{3}$.

Note: The slope of a line can be positive, negative, zero or undefined.
i) Positive slope: Here, y increases as x increases, so the line slopes upwards to the right. The slope will be a positive number.
ii) Negative slope: Here, y decreases as x increases, so the line slopes downwards to the right. The slope will be a negative number.
iii) Zero slope: Here, y does not change as x increases, so the line is exactly horizontal. The slope of any horizontal line is always zero.
iv) Undefined slope: When the line is exactly vertical, it does not have a defined slope. The two x coordinates are the same, so the difference is zero.