Question 79273
<pre>
what is the slope-intercept form of the line passing through the point (6,-9) and parallel to the line 5x-7y=-1


Slope - Intercept Form 
          y = mx + b , where m = slope and b = y-intercept


We can find the slope of the line passing through (6, -9) and parallel
to the line 5x - 7y = -1, by finding the slope of the line parallel to it.
That is 5x - 7y = -1.   

Find the slope of 5x - 7y = -1
                  5x + 1 = 7y
                  5       1
                 ___x  + ____ = y
                  7       7

Slope or m = 5/7

Since the two line are parallel, they have the same slope
so the slope of the line passing through (6,-9) and parallel to
the line 5x - 7y = -1 is 5/7.


Now, we will find the b, the y - intercept.

           y = mx + b, where m= 5/7 and x = 6 and y = -9
          -9 = 5/7(6) + b
          -9 = 30/7 + b
       -9 - 30/7 = b
          -72/7 = b

The slope - intercept form of the new line is 

          y = (5/7)x - 72/7



{{{graph (200, 200, -10, 5, -15, 3, (5/7)x + (1/7), (5/7)x - (72/7))}}}