Answer:
Explanation:
Part A: The slope of a linear function represents the rate of change between two points on the graph. In this case, we can calculate the slope by finding the change in the balance (g(x)) divided by the change in the number of days (x).
Let's take the first two points (0, $325) and (5, $400). The change in the balance is $400 - $325 = $75, and the change in the number of days is 5 - 0 = 5.
So, the slope of the function is 75/5 = $15.
Interpretation: This means that for every day that passes, the balance in the bank account increases by $15.
Part B:
Point-slope form:
To write the equation of the line in point-slope form, we can use one of the points given in the table and the slope we calculated. Let's use the point (0, $325) and the slope $15.
The point-slope form is: g(x) - g(0) = m(x - 0), where m is the slope and (0, g(0)) is a point on the line.
Substituting the values, we get: g(x) - $325 = $15x
Slope-intercept form:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. In this case, since g(x) represents the balance and y represents the balance, we can rewrite the equation as g(x) = mx + b.
Using the slope we calculated ($15) and one of the points (0, $325), we can substitute the values to find the equation.
Substituting the values, we get: g(x) = $15x + $325
Standard form:
The standard form of a linear equation is Ax + By = C, where A, B, and C are constants.
To convert the equation to standard form, we rearrange the equation in slope-intercept form to the standard form.
Using the equation we found in slope-intercept form (g(x) = $15x + $325), we can rearrange it to the standard form: -$15x + g(x) = -$325
Part C:
To write the equation of the line using function notation, we can replace g(x) with y in any of the forms we found in Part B.
For example, using the slope-intercept form, we can write the equation as y = $15x + $325.
Part D:
To find the balance in the bank account after 12 days, we can substitute x = 12 into the equation we found in Part B.
Using the slope-intercept form equation (g(x) = $15x + $325), we can substitute x = 12:
g(12) = $15(12) + $325
g(12) = $180 + $325
g(12) = $505
Therefore, the balance in the bank account after 12 days is $505.