Answer: The required slope of the given function is [tex]-\dfrac{a}{b}.[/tex]
Step-by-step explanation: We are given the following function that represents a straight line :
[tex]L:ax+by+c=0,b\neq0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We are to find the slope of the given function.
We know that
the slope-intercept form of a linear function is given by
[tex]y=mx+c,[/tex] where m is the slope and c is the y-intercept of the function.
From equation (i), we get
[tex]ax+by+c=0\\\\\Rightarrow by=-ax-c\\\\\Rightarrow y=-\dfrac{a}{b}x-\dfrac{c}{b}~~~~~~~~~~~~~~~~~~~~~~[\textup{since }b\neq0][/tex]
Comparing the above equation with the slope-intercept form, we get
[tex]m=-\dfrac{a}{b}.[/tex]
Thus, the required slope of the given function is [tex]-\dfrac{a}{b}.[/tex]
