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Question

Question: How do you write \(2x+3y=6,\) in slope intercept form....

How do you write 2x+3y=6,2x+3y=6, in slope intercept form.

Explanation

Solution

Rewrite the given equation in form of general equation of slope intercept form, i.e. y=mx+c,y=mx+c, then compare the obtained equation with general equation and determine the value of m'm' i.e. gradient of line or slope of line and c'c' then draw the graph of equation.

Complete step by step solution:
As per data given in the question,
Here we have,
2x+3y=62x+3y=6
As, we have to represent the above equation in slope intercept form.
We know that,
In slope intercept form,
Any equation is represented in form of y=mx+cy=mx+c
So, representing the given equation in form of general equation of slope intercept form,
We will get,
2x+3y=62x+3y=6
3y=2x+6\Rightarrow 3y=-2x+6
y=2x+63\Rightarrow y=\dfrac{-2x+6}{3}
Now converting the obtained equation, we will get,
y=2x3+63y=\dfrac{-2x}{3}+\dfrac{6}{3}
y=23x+2...(i)\Rightarrow y=\dfrac{-2}{3}x+2...(i)
Comparing equation (i)(i) with general equation of slope intercept form,
We will get,

Value of m=23m=\dfrac{-2}{3} hence, we can say that line have a gradient of 23\dfrac{-2}{3} value of c'c'value of yy intercept is 22 means the line cuts yy-axis at 2.2.

Note: Always represent the given equation in the form of a general slope. Intercept form
i.e. y=mx+c,y=mx+c,
mm is called the gradient of line.
While representing the equation in y=mx+c,y=mx+c, do not ignore the sign of m'm' as mm can be positive or negative.