The equation of the line is y = ax + b
At the point 2,2: 2 = 2a + b, so b = 2 - 2a
The y intercept occurs at x = 0, so int(y) = b
The x intercept occurs y = 0, so 0 = ax + b and int(x) = -b/a
The sum int(y) + int(x) = b - b/a = 9.
Plug in b = 2 - 2a to get 2 - 2a - 2/a + 2 = 9
2*(a + 1/a) = -5
2a^2 + 5a + 2 = 0
solve for a, then put into b = 2 - 2a to get b
a = (-5 ± √[25 - 4*2*2]) / 4 = (-5 ± 3)/4
a = -2 or -1/2
SInce b = 2 - 2a,
for a = -2, b = 2 + 4 = 6
for a = -1/2, b = 2 + 1 = 3
The equations are
y = -2x + 6 or y = -(1/2)x + 3
Check: set x = 2: this gives y = 2 for both eqs.
y intercept is 6 or 3
x intercept is 3 or 6
in either case the sum is 9. So both equations work.
2007-12-17 19:07:52
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answer #1
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answered by gp4rts 7
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