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.)

  c = 30t +50

Step-by-step 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

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.