Answer:
In this problem, we are looking for an equation in the form of y = mx + b that describes the situation where a bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.
To find the equation, we need to find the slope (m) and the y-intercept (b). The y-intercept is the point at which the line crosses the y-axis, which in this case is the initial amount of money in the account ($50). The slope is the rate at which the amount of money in the account is changing over time.
To find the slope, we can use the following formula:
slope = (y2 - y1) / (x2 - x1)
In this case, y2 is the total amount of money in the account after 12 weeks ($275), y1 is the initial amount of money in the account ($50), x2 is the number of weeks after the account is opened (12 weeks), and x1 is the number of weeks before the account is opened (0 weeks).
Plugging these values into the formula, we get:
slope = (275 - 50) / (12 - 0) = 225 / 12 = 18.75
Now that we have the slope, we can plug it into the equation y = mx + b, along with the y-intercept (b = 50), to get the final equation:
y = 18.75x + 50
This equation represents the situation described in the problem, where the bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.