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A line has gradient 6 and passes through the points with coordinates (-1,6) and (7,a). Find the value of a

Verified Answer :

luana

\(General\ formula\ for\ line:\\\\y=ax+b,\ where\ a-gradient\\\\y=6x+b\\\\Substitute\ point\ (-1,6):\\\\6=6\cdot(-1)+b\\6=-6+b\\b=6+6\\b=12\\\\y=6x+12\\\\Substitute\ point\ (7,a)\\\\a=6\cdot7+12\\a=42+12=54\)

olemakpadu

We can also see it this way: 

Noting that point in the form  (x, y)
(-1, 6)  and (7, a) .  x1 = -1, y1 = 6,  x2 = 7, y2 = a
Gradient , m =  (y2- y1) / (x2 - x1).  m =6.
Substituting:

6 =  (a - 6) / (7 - -1)
6 =  (a -6) / (7+1)
6 = (a -6) /8    Cross Multiplying
48 = a -6.
48 +6 = a.
54 = a.
Therefore a = 54.
I hope this helps.

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