Suppose y is directly proportional to x and that y = 40 when x=5.
Complete parts (a)and(b).
Find the constant of proportional k.
k=
(b)use y=ky to find y when x=9
y=
40 = 5 k
so
k = 8
y = 8 x
y(9) = 8*9 = 80 - 8 = 72
To find the constant of proportionality (k), we are given that y is directly proportional to x. This means that the ratio of y to x remains constant. We can use the given information to find the value of k.
(a) To find k, we can use the formula for direct variation: y = kx. By substituting the known values y = 40 and x = 5 into the equation, we can solve for k.
40 = k * 5
Dividing both sides of the equation by 5:
8 = k
Therefore, the constant of proportionality (k) is equal to 8.
(b) Now that we have the value of k, we can use the formula y = ky to find the value of y when x = 9.
Substituting the value of k into the equation:
y = 8 * 9
Simplifying:
y = 72
Therefore, when x = 9, y = 72.