Question

You have a linear function g(x) representing the balance in a bank account, where x is the number of days that have passed. The table of values for this function is as follows:

x: 0, 3, 6
g(x): $600, $720, $840

Now, answer the following:
A) Find and interpret the slope of the function.
B) Write the equation of the line in point-slope, intercept-slope, and standard forms.
C) Write the equation of the line using function notation.
D) What is the balance in the bank account after 7 days?

Answer 1

A linear function represents the balance in a bank account. The slope of the function represents the rate of change, which in this case is $40 per day. The equation of the line can be written in point-slope, intercept-slope, and standard forms. The balance in the bank account after 7 days is $880.

Step-by-step explanation:

A) The slope of a linear function represents the rate of change. To find the slope of the function, we use the formula: slope = (change in y)/(change in x). In this case, the change in y is $120 and the change in x is 3 days. So, the slope of the function is $120/3 = $40 per day. This means that the balance in the bank account is increasing by $40 per day.

B) Point-slope form: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Using the point (0, $600) and the slope $40, the equation in point-slope form is: y - $600 = $40(x - 0). Simplifying, we get: y - $600 = $40x.

Intercept-slope form: y = mx + b, where m is the slope and b is the y-intercept. Using the slope $40 and the y-intercept $600, the equation in intercept-slope form is: y = $40x + $600.

Standard form: Ax + By = C. Rearranging the intercept-slope form, we get: -$40x + y = $600. Multiplying through by -1, we get: $40x - y = -$600.

C) The equation of the line using function notation is g(x) = $40x + $600.

D) To find the balance in the bank account after 7 days, substitute x = 7 into the function g(x) = $40x + $600. Evaluating, we get g(7) = $40(7) + $600 = $280 + $600 = $880.