```Question 75295
<pre>
Graph this equation 3 ways 2x+3y=1

1. Make a table of values of x and y. Assume values of x
then substitute them to 2x + 3y = 1. Plot the points
connect with a line.

If x = -2                         if x = 2

2(-1) + 3y = 1              2(2) + 3y = 1
-2 + 3y = 1                4  + 3y = 1
3y = 3                     3y = -3
y = 1                      y = -1

x      y
-1      1
2     -1

Plot the two point (-2, 1) and (2, -1)

{{{graph (200, 200, -4, 5, -5, 4, (-2/3)x +1/3)}}}

2. Locate x and y intercept. x -intercept crosses x axis so y = 0
y - intercept crosses y-axis so x = 0

x - intercept                    y -intercept

2x + 3(0) = 1                   2(0) + 3y = 1
2x = 1                          3y = 1
x = 1/2                         y = 1/3

Plot the two points (1/2, 0) and (0, 1/3)

{{{graph (200, 200, -1, 2, -2, 2, (-2/3)x + 1/3)}}}

3. Slope and y - intercept. Find the slope and y -intercept of the equation
y = mx + b where m = slope and b = y-intercept

2x + 3y =1
3y = -2x + 1
y = (-2/3)x + 1/3
m = -2/3  b = 1/3

Plot the first point using the y-intercept (0, 1/3)
then with the help of the slope we will locate the second point
the numerator indicated the change in y. Move up if the numerator is positive
move down if it is negative. the denominator indicates the change in x.
if positive, move right. negative, move left

from (0, 1/3) move 2 units down then 3 units right so the new point is located
(3, -1 1/3)

{{{graph (200, 200, -1, 4, -2, 2, (-2/3)x + 1/3)}}}

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