Question

How do you find the slope and the $y$ intercept for: $x + 8y = 0$?

Answer 1

Hint: First of all this is a very simple and a very easy problem. The general equation of a slope-intercept form of a straight line is $y = mx + c$, where $m$ is the gradient and $y = c$ is the value where the line cuts the y-axis. The number $c$ is called the intercept on the y-axis. Based on this provided information we try to find the equation of the straight line.

Complete step-by-step solution:
We are given that an equation of a line is given by $x + 8y = 0$.
Now consider the given equation, as shown below:
$ \Rightarrow x + 8y = 0$
Here the slope of the equation is obtained when expressed the given equation in slope-intercept form as given below:
Rearrange the equation such that the $y$ term is on the left hand side of the equation, whereas the $x$ term and the constant 0 is on the right hand side of the equation, as given below:
$ \Rightarrow 8y = - x + 0$
Now divide the above equation by 8, so as to remove the coefficient of the $y$ term on the left hand side of the equation, as given below:
$ \Rightarrow y = \dfrac{{ - 1}}{8}x + 0$
Here the above equation is expressed in the form of the slope intercept form which is $y = mx + c$.
The slope of the equation is given by:
$ \Rightarrow m = \dfrac{{ - 1}}{8}$
Whereas the y-intercept is given by:
$ \Rightarrow c = 0$
The intercept is zero. Hence the line is passing through the origin with a negative slope.

The slope and the $y$ intercept of $x + 8y = 0$ are $\dfrac{{ - 1}}{8}$ and $0$.

Note: Please note that while solving such kind of problems, we should understand that if the y-intercept value is zero, then the straight line is passing through the origin, which is in the equation of $y = mx + c$, if $c = 0$, then the equation becomes $y = mx$, and this line passes through the origin, whether the slope is positive or negative.