Math problems?

Question

the table shown represents a linear function. what is the value of "t" when h=157?
t=1 2 3 ?
h=2 7 12 157

Answer 1

Start with the 3 terms you know:
t = 1 --> h = 2
t = 2 --> h = 7
t = 3 --> h = 12

Each time you increase t by 1, h goes up by 5. That means you will have h = 5t + b. It should be easy to see that b = -3.

Therefore the formula for h would be:
h = 5t - 3

t = 1:
h = 5(1) - 3
h = 2

t = 2:
h = 5(2) - 3
h = 7

t = 3:
h = 5(3) - 3
h = 12

Now plug in h = 157 and solve for t:
157 = 5t - 3

Add 3 to both sides:
160 = 5t

Divide both sides by 5:
160 / 5 = t
t = 32

Answer 2

You need some commas between values to show the exact correspondence. You want a linear function, not an exponential function as in the first solution. However you only need two sets of points for a linear function. Check to be sure you are not asked for a quadratic function.

Linear functions are of the form ax + by = c or, if you solve for x, y = mx + b. With x=t and y=h, substitute the known values and determine a,b,c or m and b .