Question

How do you write the equation in slope intercept form given $6x-2y=12$?

Answer 1

We know that slope intercept form is the general form for linear equations. It emphasizes the slope and the y-intercept of the line. The slope intercept form of the equation of the straight line is $y=mx+c$. To write the given equation in slope intercept form, we will transpose the terms to get the value of y.

Complete step-by-step solution:
We are given an equation $6x-2y=12$ and are asked to write it in the slope intercept form. We know that the equation of a line in slope intercept form is given by the expression,
$y=mx+c$ …. (1)
where m is the slope and c is the y-intercept.
To convert the given linear equation $6x-2y=12$ to slope intercept form, we have to transpose terms to get the value of y.
Hence, we will transpose the term containing x to RHS, which makes it,
$\Rightarrow -2y=-6x+12$ …. (2)
And to get the value of y, let us divide both sides of equation (2) by -2, so, we get,
$\Rightarrow \dfrac{-2y}{2}=\dfrac{-6x}{2}+\dfrac{12}{2}$
$\Rightarrow -y=-3x+6$ ….. (3)
Multiplying both the sides of equation (3) by -1, we get,
$\Rightarrow y=3x-6$
Hence the slope intercept form of the given equation $6x-2y=12$ is $y=3x-6$.

Note: We must note that the slope-intercept form is the most popular form of a straight line due to it being simple. We can easily describe the characteristics of the straight line even without seeing its graph because the slope m and y-intercept can easily be identified or read from this form. Though this seems easy to solve, we must take care to be careful of the terms and the signs while transposing the terms to get the value of y. There are chances that we may miss out on the negative sign in equation (3) and may write the value as y = 3x + 6. Most important if we don’t remember the general form of the slope intercept form, we will not be able to solve this.