Y varies directly as x . If y is 2 when x is 8, then the constant of variation is 1/4 . True or False
2 answers:
Answer:
The answer is TRUE.
Step-by-step explanation:
In order to determine the answer, we have to know about the directly proportional. The directly proportional is when two variables increase at the same time. If one variable is increased, so the other one will be increase too.
The ratio of both is a constant, it is called "constant of variation".
For example:
A varies directly as B, so:
where k is the constant of variation
In this case, we have that Y varies directly as X. Also if Y is 2 when X is 8, the constant of variation is:
Finally, according to the value of the constant of variation, the statement is TRUE.
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Answer:
5x -7y = 21
Step-by-step explanation:
A sketch can convince you that BC is a transversal perpendicular to parallel lines AB and CD. The question asks for an equation for CD, so we just need to write the equation of a line through D that is parallel to AB.
One way to do this is to equate the slopes of the parallel lines:
∆y/∆x for AB = ∆y/∆x for CD
(y2 -y1)/(x2 -x1) = (y -2)/(x -7) . . . . . . where (x1, y1) = A; (x2, y2) = B; (7, 2) = D
(4 -(-1))/(1 -(-6)) = (y -2)/(x -7)
5(x -7) = 7(y -2) . . . . . . . . . . . . . cross multiply
5x -7y = 21 . . . . . . . . . . . . . . . . add 35 -7y, simplify
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Note that the graph shows the line CD is named "b", and its equation is shown at upper left. Multiplying that equation by -1 gives the one shown here.
