Answer: $1,125.
Explanation:
Part A: The slope of a linear function represents the rate of change, or how much the dependent variable (in this case, the balance in the bank account) changes for each unit increase in the independent variable (the number of days). To find the slope, we can use the formula:
slope = (change in y) / (change in x)
Let's choose two points from the table of values, (0, $1,500) and (4, $1,200), to calculate the slope:
(change in y) = ($1,200 - $1,500) = -$300
(change in x) = (4 - 0) = 4
slope = (-$300) / 4 = -$75
The slope of the function is -$75. This means that for each additional day that passes, the balance in the bank account decreases by $75.
Part B: To write the equation of the line, we can use different forms:
1. Point-slope form: y - y1 = m(x - x1)
Using the point (0, $1,500) and the slope -$75, we get:
y - $1,500 = -$75(x - 0)
Simplifying:
y - $1,500 = -$75x
This is the equation in point-slope form.
2. Slope-intercept form: y = mx + b
Using the slope -$75 and the point (0, $1,500), we can substitute these values into the equation:
y = -$75x + $1,500
This is the equation in slope-intercept form.
3. Standard form: Ax + By = C
Rearranging the equation in slope-intercept form, we get:
$75x + y = $1,500
Multiplying by 100 to eliminate decimals:
7500x + 100y = 150,000
This is the equation in standard form.
Part C: In function notation, the equation of the line is:
g(x) = -$75x + $1,500
This represents that the balance in the bank account, g(x), is a function of the number of days, x.
Part D: To find the balance in the bank account after 5 days, we can substitute x = 5 into the equation of the line. Using the equation in slope-intercept form:
y = -$75x + $1,500
Substituting x = 5:
y = -$75(5) + $1,500
Simplifying:
y = -$375 + $1,500
y = $1,125
After 5 days, the balance in the bank account would be $1,125.
Overall, that's a lot of money, lol. Hope this helps.