Question 115695
To know the slope of the line 5x-6y=-1, let's 'convert' this to slope-intercept form y=mx+b

where m is the slope and b is the y-intercept


5x-6y=-1
-6y=-5x-1
6y=5x+1
y=5x/6+1/6

Thus, the slope of the given line and the unknown line must be 5/6

But, it has an x-intercept of 4 . That means that it passes through (4,0)

y=mx+b

GIVen: m=5/6, x=4, y=0

0=(5/6)(4)+b
0=10/3+b
b=-10/3

Substituting, 

y=mx+b

y=5x/6-10/3

Multiply both sides by 6

6y=5x-20

The equation of the line is 5x-6y-20=0

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