Question 74223
<pre>
graph 
a) by finding the x- and y-intercept : x-3y=-6

Two points determine a line.WE need two points then.
The x-intercept and the y-intercept
To find x-intercept , y = 0. Substitute it to x-3y=-6

             x - 3(0) = -6
                    x = -6
First point is located (-6,0)

To find y -intercept, x = 0.Substitute it to x-3y=-6

              0 - 3y = -6
                 -3y = -6
                   y = 2

second point is located (0, 2)

graphing time

{{{graph (200, 200, -8, 3, -3, 6, (1/3)x + 2)}}}

 
            


b)by using the slope and y-intercept : x-4y=-8

Slope - intercept form is y = mx + b, where m = slope and b = y-intercept

we will rewrite the given equation to slope - intercept form

                  x + 8 = 4y
                  
                  x     8
                 ___ + ___  = y
                  4     4

                  1     
                 ___x + 2  = y
                  4     


m = 1/4 and b = 2

 The first point is located using b which is the y - intercept (0,2)

Using the y -intercept, the slope help us locate the next point
The numerator represents the change in y and denominator the change in x

from (0,2) we move 1 unit up (up for positive)
 and 4 unit right (right for positive)


{{{graph (200, 200, -3, 5, -2, 7, (1/4)x + 2)}}}