What is the slope and intercept for # 2x+3y=9# and how would you graph it?

1 Answer
Oct 7, 2015

Answer:

#m=-2/3#

#c=9#

Explanation:

A straight line graph is of the form:

#y=mx+c#

#m# is the gradient

#c# is the intercept which is the point at #x=0# where the line cuts the #y# axis.

So we get our equation into this form:

#2x+3y=9#

#3y=-2x+9#

#y=-2/3x+9#

So the slope or gradient #m=-2/3#

The intercept #c=9#

To graph it manually just pick a range of values of #x# and find the corresponding value of #y#.

e.g #x=1rArr#

#y=-(2/3xx1)+9= =25/3#

So your 1st point is #[1,25/3]#

You should end up with this:

graph{-2/3x+9 [-16.5, 23.5, -8.7, 11.3]}