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)

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facundo3141592 facundo3141592 · Answer 1 · 2022-07-11T17:16:41+02:00

The answers are:

a) s = -$75

b) y = -$75*x + $1500

c) y = g(x) = -$75*x + $1500

d) y = g(5) = $1125

Remember that if a line passes through the points (a, b) and (c, d), then the slope is:

[tex]s = \frac{d - b}{c - a}[/tex]

In this case, we can use two of the points on the table, for example, the first two:

(0, 1500) and (2, 1350).

Then the slope is:

[tex]s = \frac{1350 - 1500}{2 - 0} = -75[/tex]

This means that for each day that passes, the balance in the bank account decreases by $75.

b) The linear equation is:

y = -$75*x + k

the slope that we already know, and k is the value that the line takes when x = 0.

On the table we can see that when x = 0, g(x) = $1500, then:

y = -$75*x + $1500

In standard form we have:

y + $75*x = $1500

c) The function notation is just:

y = g(x) = -$75*x + $1500

So we clarify that y is the dependent variable and x the independent variable.

d) The balance after 5 days is:

y = g(5) = -$75*5 + $1500 = $1,125

If you want to learn more about linear equations:

https://brainly.com/question/1884491

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