Question

How do you write an equation of a line with slope $3$ and the $y$ intercept is -4 ?

Answer 1

First of all this is a very simple and a very easy problem. The general equation 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 answer:
Given that an equation of a line has the slope equal to 3 and the $y$intercept equal to -4.
We know that the equation of the straight line is given by:
$\Rightarrow y = mx + c$
Where $m$ is the slope of the straight line and $c$ is the $y$intercept of the straight line.
So given that the slope of the straight line is $m = 3$
The intercept of the straight line is $c = - 4$
Substituting the values of the given data, in the general form of the straight line, as shown below:
$\Rightarrow y = mx + c$
$\Rightarrow y = \left( 3 \right)x + - 4$
So the equation of the straight line is given by:
$\Rightarrow y = 3x - 4$
On further simplifying where, moving all the variable terms and the constants to one side of the equation, as shown below:
$\Rightarrow 3x - y - 4 = 0$

Final Answer: The equation of the line is $3x - y - 4 = 0$.

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.