Question

for questions 37 - 38: landon opened a new credit card to purchase a $500 television. the graph below shows the balance on the card each month after purchasing for the first nine months, along with a best - fitting line.

1. use the points (0, 500) and (5, 740) to write an equation for the line of best fit.
2. if this trend continues, estimate the balance on the card after three years.
3. y = x+
4. y = $

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given \((x_1,y_1)=(0,500)\) and \((x_2,y_2)=(5,740)\), then \(m=\frac{740 - 500}{5-0}=\frac{240}{5}=48\).

Step2: Determine the y - intercept

The equation of a line is \(y = mx + b\). When \(x = 0\), \(y=b\). From the point \((0,500)\), \(b = 500\). So the equation of the line is \(y=48x + 500\).

Step3: Convert 3 years to months

Since 1 year has 12 months, 3 years have \(x=3\times12 = 36\) months.

Step4: Substitute \(x = 36\) into the equation

Substitute \(x = 36\) into \(y=48x + 500\). Then \(y=48\times36+500\). First, \(48\times36=(50 - 2)\times36=50\times36-2\times36=1800 - 72 = 1728\). Then \(y=1728+500=2228\).

Answer:

1. \(y = 48x+500\)
2. \(y=\$2228\)