Algebra 1 help needed please!!!

Question

Hair grows on your head faster than any other place on your body. Sue was interested in figuring out how fast her hair grows so she measured the growth. After 15 days her hair grew 3 mm. After 50 days, it grew 10 mm. If hair growth can be represented by a linear growth, then

a) write a function for the growth G(x) as a function of x= number of days

b) how long did it take Sue's hair to grow 17 mm?

Answer 1

Think LINEar.

The equation of a line is: Y = mX + B

Let the "X AXIS" = the number of DAYS.

Let the "Y AXIS" or G(X) = hair length

Now, derive to the two coordinates representing the given information: (DAYS, LENGTH)

(15, 3) and (50, 10)

Next, determine the SLOPE of the line, m, which is the RISE/RUN:

m = (10 - 3)/(50 - 15) = 7/35 = 1/5

Pick either coordinate/point, and substitute into Y = mX + B to solve for B(the Y-INTERCEPT):

Pick (50, 10) which means X=50 and Y=10.

10 = (1/5)(50) + B by substituting into the equation of a line. (Y = mX + B)

10 = 10 + B. (One-fifth of 50 is 10.)

B = 0 (Subtracting 10 from both sides.)

So, the equation of the line is: Y = (1/5)X + B

Y = (1/5)X + 0

Y = (1/5)X

Since Y is really G(X), then ANSWER (a) IS: G(X) = (1/5)X

b) how long did it take Sue's hair to grow 17 mm?

17 = (1/5)X Plugging in 17 for G(X) into Y = (1/5)X.

(5)(17) = (1/5)(5)(X) Multiply both sides by 5 to isolate the X.

85 = X

ANSWER (b) IS: 85 days for hair to grow 17 mm.

CHECKING:

Plug in X=85 and Y=17 into our LINEar equation.

Y = (1/5)X

17 ? (1/5)(85)

17 ? 17

17 = 17

Hope this was helpful Anna.

BTW, you will have at least one of these, and perhaps two, on your SAT MATH test.