Question

Given line L = ax + by + c = 0, b 0 What is the slope of this function?

Answer 1

Answer:  The required slope of the given function is $-\dfrac{a}{b}.$

Step-by-step explanation:  We are given the following function that represents a straight line :

$L:ax+by+c=0,b\neq0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the slope of the given function.

We know that

the slope-intercept form of a linear function is given by

$y=mx+c,$ where m is the slope and c is the y-intercept of the function.

From equation (i), we get

$ax+by+c=0\\\\\Rightarrow by=-ax-c\\\\\Rightarrow y=-\dfrac{a}{b}x-\dfrac{c}{b}~~~~~~~~~~~~~~~~~~~~~~[\textup{since }b\neq0]$

Comparing the above equation with the slope-intercept form, we get

$m=-\dfrac{a}{b}.$

Thus, the required slope of the given function is $-\dfrac{a}{b}.$

Answer 2

Hello,

ax+by+c=0
==> by=-ax-c  if b≠0
==>y=-a/b*x -c/b

Slope is -a/b