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# How do you put $2x - 3y = 6$ in slope-intercept form?

Last updated date: 17th Jul 2024
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Hint: The above question is based on the concept of slope-intercept form. The main approach towards solving the equation is by applying the formula of the equation of straight line. So, using this formula we need to write the equation in that form by shifting the terms on the other side.

One of the forms of the equation of a straight line is also called slope intercept form. We know the equation of straight line in slope intercept form is $y = mx + c$
Where m denotes the slope of the line and c is the y-intercept of the line.
The standard equation of first degree is $Ax + By + C = 0$ can be written in the slope intercept form as :
$y = \left( { - \dfrac{A}{B}} \right)x - \left( {\dfrac{C}{B}} \right)$
where $m = \left( { - \dfrac{A}{B}} \right)$ and $c = \left( { - \dfrac{C}{B}} \right)$
and also $B \ne 0$ .
So now the given equation is $2x - 3y = 6$
So first we need to shift the terms which are on the left-hand side towards the right hand side.
Therefore, we get
$\Rightarrow 2x - 3y = 6 \\ \Rightarrow - 3y = - 2x + 6 \\$
Then by multiplying it with negative sign throughout the equation we get,
$3y = 2x - 6$
Then we need to isolate the term y so we shift the number 3 on the right hand side to the denominator.
$y = \dfrac{2}{3}x - 2$
Hence the standard equation of first degree is written in the above slope intercept form
So, the correct answer is “$y = \dfrac{2}{3}x - 2$ ”.

Note: An important thing to note is that here the c=-2 i.e., the y-intercept of the equation is -2.In the graph we plot the equation we get to know that the equation of line will cut y-axis at -2 and the slope which is $\dfrac{2}{3}$ which gives the direction of the line.