Question

How do you find slope and intercept of \[\mathbf{4x}-\mathbf{2y}=\mathbf{12}\]?

Answer 1

Hint: Convert the given equation in form of slope intercept form
Which is $y=mx+c$
Where, $m$ is the slope
$c$ is the $y$ intercept.
Then determine the value of slope and value of \[y\]– intercept by comparing the converting equation with the general slope intercept form.

Complete step-by-step solution:
As per data given in the question,
We have,
\[4x-2y=12\]
As we know that,
The general expression of slope intercept form is,
$y=mx+c...(1)$
Where, $m$ is the slope
\[c\] is the $y$ intercept.
So, converting the given equation,
We will get,
\[4x=12+2y\]
\[\Rightarrow 2y=4x-12\]
As here we get the equation in terms of \[2y\]. So converting the equation in form of \[y\] for that shifting the \[2\] from left side of equation to the right side of equation,
We will get,
\[y=\left( 4x-12 \right)/2\]
So, value of equation will be,
$y=2x+2...(2)$
Hence,
Now comparing both equation \[\left( 1 \right)\] and \[\left( 2 \right)\],
We will get,
Value of \[m\] i.e. slope of the graph is \[2\].
And the value of “\[y\]- intercept” i.e. value of \[c\] will be \[-6\].

Hence, the slope of the given equation will be \[2\] and it’s \[y\] – intercept will be \[-6\].

Note: Slope intercept form is a form of writing an equation of a straight line.
We can also term slope as gradient.
While we write any equation in this form, we usually get information regarding the equation of the line and the value of slope and intercept of the line.
The slope of the line may be either positive, negative or zero.
If the slope of line is positive it means that the slope upwards from left to right and if the slope of line is negative it means that slope downwards from left to right. if the slope of the line is zero it means that slope will be parallel to the horizontal line.