SOLUTION: What is the equation of the line that passes through (-2,3)and is parallel to 2x+3y=6?

Question 567501: What is the equation of the line that passes through (-2,3)and is parallel to 2x+3y=6?
Found 2 solutions by mananth, nyc_function:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
2 x + 3 y = 6
Find the slope of this line
make y the subject
3 y = -2 x + 6
Divide by 3
y = - 2/ 3 x + 2
Compare this equation with y=mx+b
slope m = - 2/ 3
The slope of a line parallel to the above line will be the same
The slope of the required line will be - 2/ 3
m= - 2/ 3 ,point ( -2 , 3 )
Find b by plugging the values of m & the point in y=mx+b

3 = 4/ 3 + b
b= 5/ 3
m= - 2/3
Plug value of the slope and b in y = mx +b
The required equation is y =- 2/3x+5/3

m.ananth@hotmail.ca

Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
Solving 2x + 3y = 6 for y, we get y = (-2/3)x + 2.
The slope is the coefficient of x,which in this case is -2/3.
We now use the point-slope formula y - y1 = m(x - x1) and the given point.

y - 3 = (-2/3)(x - (-2))

y - 3 = (-2/3)x - 4/3

y = (-2/3)x - 4/3 + 3

y = (-2/3)x + 5/3

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