Question

Coach keller is having the last names of his players printed on their shirts!?

Answer 1

Here, x represents the number of letters, and y represents the costs in dollars.

Slope defined as the change in the y-variable to the change in the x-variables;

It is given by:

`\text{Slope}(m)= (y_2-y_1)/(x_2-x_1)`

Consider any two points from the given table:

(15, 7)and (30, 10.75)

Substitute the given values we have;

`\text{Slope}(m) = (10.75-7)/(30-15)=(3.75)/(15) =0.25`

The equation of any straight line is given by:

`y =mx+b` where m is the slope and b is the y-intercepts.

Substitute the value of m = 0.25 in the equation of line we have;

y = 0.25x+b

Solve for b;

Substitute any values of x and y from the given table;

For x = 20 and y = 8.25

then;

8.25 = 0.25(20) +b

Simplify:

8.25 = 5+b

Subtract 5 from both sides we have;

b = 3.25

y-intercept(b) = 3.25

Therefore, linear function become;
`y = 0.25x+3.25`

Here slope(i.,e m = 0.25) represents the cost per letter.

and y-intercept of the function represents the initial cost