Write an equation in slope-intercept form fo each situation. Assume a linear relationship between x and y.
In 2007 Tamara bank account balance was $500. In 2010, it was $1,400. Assuming she saves the same amount each year, in what year will her balance be 3,500?
Thank you so much I found my mistake l added 10 to 2010
To find the equation in slope-intercept form that represents the relationship between the year (x) and Tamara's bank account balance (y), we can use the formula:
y = mx + b
Where:
y = bank account balance
m = slope (rate of change - how much the balance increases each year)
x = year
b = y-intercept (starting balance in the year 2007)
To determine the slope (m), we can use the given information that Tamara's bank account balance increased from $500 in 2007 to $1,400 in 2010. We can calculate the change in balance over the three-year period:
Change in balance = Final balance - Initial balance
Change in balance = $1,400 - $500
Change in balance = $900
Since the problem states that Tamara saves the same amount each year, we can divide the change in balance by the number of years (3) to find the rate of change or slope (m):
Slope (m) = Change in balance / Number of years
Slope (m) = $900 / 3
Slope (m) = $300
Now that we know the slope (m), we can determine the y-intercept (b) using the initial balance in 2007:
y = mx + b
$500 = $300 * 2007 + b
Solving for b:
$500 = $602,100 + b
b = $500 - $602,100
b = -$601,600
Now we have the slope (m) and the y-intercept (b), so we can substitute these values into the equation:
y = $300x - $601,600
To find the year when Tamara's balance will be $3,500, we can substitute the balance (y) into the equation and solve for the year (x):
$3,500 = $300x - $601,600
Now, we can solve for x:
$300x = $3,500 + $601,600
$300x = $605,100
x = $605,100 / $300
x ≈ 2,017
Therefore, Tamara's balance will be $3,500 in the year 2017.
If year 0 is 2007 then the y intercept is $500.
Since we know that 3 years after year 0 her balance was $1400, we determine that her balance increased by $900 ($1400-$500 = $900)
So the rate of increase is $300 per year ($900/3 =$300)
So the equation would be y=$300x + $500.
In trying to determine how many years (x) it will be for her bank account balance(y) to equal $3500 we input $3500 in for y in the equation and solve for x.
$3500 = $300x + $500
$3500 - $500 = $300x + $500 - $500
$3000/$300 = $300x/$300
x = 10 years
2007 + 10 years = 2017