Question

In the first year of her practice, a family counselor saw 80 clients. In the second year, the number of clients grew to 110. If a linear trend continues, write an equation that gives the number of clients c the counselor will have t years after beginning her practice. (Assume t = 1 for the first year.)

Answer 1

c = 30t +50

Explanation:

The number of clients grew at the rate of 30 per year. Since we know that ...

(t, c) = (1, 80) . . . . . . independent variable t; dependent variable c

we can use a point-slope form of the equation of the line:

y = m(x -h) +k . . . . . line with slope m through point (h, k)

c = 30(t -1) +80

Simplifying, this becomes ...

c = 30t +50