Question

Tina just opened a new restaurant. She earned $550 on

Answer 1

Answer:

Samantha will earn $1,150 on the 7th day.

Step-by-step explanation:

Linear Modeling

It consists of finding the equation of a line that represents the data provided in a specific situation.

Tina's (or Samantha's) earnings are $550, x, $750,... where x is an unknown amount for the second day of her new restaurant.

The earnings continue to increase at the same rate until the 7th day. We must find the earnings for that last day.

The linear model can be found in several ways. We'll use the slope-point form of the line, finding first the slope and then the y-intercept.

The equation of the line in slope-intercept form is:

y=mx+b

Being m the slope and b the y-intercept.

1) Find the slope

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

We have the points (1,550) and (3,750), thus:

$\displaystyle m=\frac{750-550}{3-1}=100$

2) Get the equation of the line

Substituting into the equation of the line, we get:

y=100x+b

Select the point (1,550), substitute into the above equation, and solve for b:

550=100(1)+b

Solving:

b=450

Thus we complete the equation of the linear model:

y=100x+450

3) Substitute 7 for x

y=100(7)+450

y=1,150

Samantha will earn $1,150 on the 7th day.