Question

The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:

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


Part A: Find and interpret the slope of the function. (3 points)

Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)

Part C: Write the equation of the line using function notation. (2 points)

Part D: What is the balance in the bank account after 7 days? (2 points)

Answer 1

Part A:
To find the slope of the function g(x), we can use the formula:

slope = (change in y) / (change in x)

Using the values given in the table, we can calculate:

slope = (g(3) - g(0)) / (3 - 0) = (720 - 600) / 3 = 40

The slope of the function g(x) is 40. This means that for each day that passes, the balance in the bank account increases by $40.

Part B:
To write the equation of the line in point-slope form, we can use the point-slope formula:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Using the point (0, 600), we can write:

g(x) - 600 = 40(x - 0)

Simplifying, we get:

g(x) = 40x + 600

This is the equation of the line in point-slope form.

To write the equation of the line in slope-intercept form, we can rearrange the equation as:

g(x) = 40x + 600 = 40(x) + b

where b is the y-intercept. From the equation, we can see that b = 600. Therefore, the equation of the line in slope-intercept form is:

g(x) = 40x + 600

To write the equation of the line in standard form, we can rearrange the equation in slope-intercept form as:

-40x + g(x) = 600

This is the equation of the line in standard form.

Part C:
To write the equation of the line using function notation, we can use the slope-intercept form:

g(x) = 40x + 600

This is the equation of the line in function notation.

Part D:
To find the balance in the bank account after 7 days, we can use the equation of the line:

g(x) = 40x + 600

Substituting x = 7, we get:

g(7) = 40(7) + 600 = 880

Therefore, the balance in the bank account after 7 days is $880.