Question 218681
Consider the following equation of a line.
2x + 3y − 6 = 0


(a) Find the slope and y-intercept (if possible) of the line specified by the equation. (If an answer is undefined, enter UNDEFINED.)


m = 2  This is the slope.  See steps below
(x,y)= (0,2)  This is the y-intercept.  See steps below.


Step 1.  The slope-intercept from is given as y=mx+b where m is the slope and b is the y-intercept at x=0 or at point (0,b).


Step 2.  Put the given equation in slope intercept form.


{{{2x+3y-6=0}}}


Add 6-2x to from both sides of the equation


{{{2x+3y-6=6-3x=0+6-2x}}}


{{{3y=-2x+6}}}


Divide 3 to both sides of equation


{{{3y/3=-2x/3+6/3}}}


{{{y=-2x/3+2}}}


Step 3.  The equation {{{y=-2x/3+2}}} has a slope m=-2/3 and y-intercept b=2 or at point(0,2).


Now the slope of {{{-2/3}}} for every 3 units you go the right, you go two units down.   

To plot the line take the y-intercept at point (0,2).  So starting at point (0,2) or x1=0 and y1=2 we go three units to the right means x2=0+3=3 and 3 units down means y2=2-2=0.  So we have two points (0,2) and (3,0).


{{{graph(400,400, -10, 10, -10, 10, -2x/3+2)}}}


I hope the above explanation was useful.


And good luck in your studies!


For free Step-By-Step Videos on Introduction to Algebra, please visit 

http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit 

http://www.FreedomUniversity.TV/courses/Trigonometry.


Respectfully,
Dr J