Answer:
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:
[tex]\text{Slope}(m)= \frac{y_2-y_1}{x_2-x_1}[/tex]
Consider any two points from the given table:
(15, 7)and (30, 10.75)
Substitute the given values we have;
[tex]\text{Slope}(m) = \frac{10.75-7}{30-15}=\frac{3.75}{15} =0.25[/tex]
The equation of any straight line is given by:
[tex]y =mx+b[/tex] 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; [tex]y = 0.25x+3.25[/tex]
Here slope(i.,e m = 0.25) represents the cost per letter.
and y-intercept of the function represents the initial cost
