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









 

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