In the xy-plane, the line with equation ax + by + c = 0, where abc ≠ 0, has slope 2/3 . What is the value of b?
(1) a = 4
(2) c = −6
Please don't forget your explanations. Thanks.
Rewrite the equation in standard form (y = mx +b); then m will be the slope:
by = -ax - c
y = (-a/b)x - c/b
So the slope of our line is -a/b, and the y-intercept is -c/b. Now we know that the slope is also equal to 2/3, so:
-a/b = 2/3
b = -3a/2
So with a we can find b, and with c we cannot. The answer is A.
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