Question

The table shows how the number of cars, c, depends on the number people, t. How would you write this as an equation?

C T
2 1
3 4
4 7
5 10

t=3c-5 t=3c+5

t=5c+3 t=5c-3

Answer 1

t = 3c - 5

Explanation:

The relation between c and t is linear as the increase of the value of t is uniform for each unit increase in the value of c.

Now, any two points on the graph of the t = f(c) equation are sufficient to determine the equation.

Let the points are (2,1) and (3,4).

So, using two points formula of straight line we get the equation is

`(t - 4)/(4 - 1) = (c - 3)/(3 - 2)`

⇒ t - 4 = 3(c - 3)

⇒ t - 4 = 3c - 9

⇒ t = 3c - 5 (Answer)