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Question: Change \(3x + 6y = 12\) into slope intercept form....

Change 3x+6y=123x + 6y = 12 into slope intercept form.

Explanation

Solution

Slope intercept form: y=mx+b,m is the slope of the liney = mx + b,{\text{m is the slope of the line}}
So here we have to convert the given equation in the form of the above equation y=mx+by = mx + b. So we need to manipulate the given equation in such a way that we can perform any arithmetic operations on both LHS and RHS equally at the same time such that the equality of the given equation doesn’t change.

Complete step by step solution:
Given
3x+6y=12.........................(i)3x + 6y = 12.........................\left( i \right)
We need to change (i) to slope intercept form which is:
y=mx+b............................(ii)y = mx + b............................\left( {ii} \right)
So to convert the given equation (i) first we have to subtract the term 3x3x to both LHS and RHS.
Such that:
⇒3x−3x+6y=12−3x ⇒6y=12−3x................(iii)  \Rightarrow 3x - 3x + 6y = 12 - 3x \\\ \Rightarrow 6y = 12 - 3x................\left( {iii} \right) \\\
Now to convert and express the equation (iii) in the form of (i) we need to isolate the term yy from the equation (iii).
For that we need to divide the equation (iii) with 6 from both LHS and RHS.
Such that:
⇒6y6=12−3x6 ⇒y=126−3x6.....................(iv)  \Rightarrow \dfrac{{6y}}{6} = \dfrac{{12 - 3x}}{6} \\\ \Rightarrow y = \dfrac{{12}}{6} - \dfrac{{3x}}{6}.....................\left( {iv} \right) \\\
Now on comparing (i) and (iv) we can say that we can get the form by simply simplifying the equation
(iv) such that:
$
\Rightarrow y = - \dfrac{{3x}}{6} + \dfrac{{12}}{6} \\
\Rightarrow y = - \dfrac{x}{2} + 2.....................\left( v \right) \\

Suchthatnowequation(v)and(iv)aresimilarnow.Alsooncomparingwecansaythat Such that now equation (v) and (iv) are similar now. Also on comparing we can say thatm = -
\dfrac{1}{2}.∗∗Thereforetheslopeinterceptformof. **Therefore the slope intercept form of 3x + 6y = 12isisy = - \dfrac{x}{2} + 2$.**

Note:
We also have an equation xa+yb=1\dfrac{x}{a} + \dfrac{y}{b} = 1 where a,ba,b are the x intercept and y intercept respectively. By using this equation we can find the x intercept and y intercept. Also while converting an equation as above one must keep in mind that the arithmetic calculations are done correctly since chances of random errors are higher in these types of questions.