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 $1,500
2 $1,350
4 $1,200


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 5 days? (2 points)

I need a good explanation for all of them ASAP!!! WILL GIVE BRAINLIEST!!!

Answer 1

Answer:

See below

Step-by-step explanation:

As per table given, the points are:

• (0, 1500), (2, 1350), (4, 1200)

Part A

Slope is found as change in range/change in domain

• m = (1350 - 1500)/(2 - 0) = - 150/2 = -75

As per the first point, we have y-intercept of 1500, when x = 0

So the function is:

• g(x) = - 75x + 1500

or

• y = -75x + 1500

Part B

Slope-intrcept form is given above

Point-slope form:

• y - y1 = m(x-x1)

This can be found as per above formula by using a pair of coordinates of one of the points or converted from slope-intercept form:

• y - 1500 = - 75(x - 0)
• y - 1500 = -75x

Standard form:

• Ax + By = C

Converting from the previous equation:

• y + 75x = 1500

Part C

The function notation is same as slope-intercept form, where y is substituted with f(x), g(x) or any other notation:

• g(x) = -75x + 1500

Part D

Balance after 5 days

• x = 5, g(x) = ?
• g(5) = -75*5 + 1500 = 1125

After 5 days the balance is going to be $1125