What is the slope-intercept form of the linear equation 2x + 3y = 6?

Solution:

The slope-intercept form of a linear equation is given by the expression:

y = mx + c------------>(1)

Where m = slope of the straight line and c is the x - intercept . The slope is further given by the expression:

m = (y₂ - y₁) / (x₂ - x₁)------------>(2)

(x₁,  y₁) and (x₂, y₂) are any two points lying on the straight line. Once the slope m is determined then the general equation of the straight line can be determined as either of the two equations below:

y - y₁ = m(x - x₁)

Or 

y - y₂ = m(x - x₂)

The equation given in the problem statement is 2x + 3y = 6. It can be rewritten in the slope-intercept form as :

3y = 6 - 2x

y =  6/3  - 2x/3

y = -2x/3 + 6/3

y =  (-2/3)x  + 2

m = -2/3 = slope

c = 2 = intercept

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What is the slope-intercept form of the linear equation 2x + 3y = 6?

Summary:

The slope-intercept form of the linear equation 2x + 3y = 6 is given by y =  (-2/3)x  + 2.