Question

the scatter plot shows leannas elevation above sea level during a hike. the trend line passes through the points (30,1070) and (75,1680). if leanna starts at 663 feet above sea level and maintains the same rate, how far above sea level will she be after one hour?
click the icon to view the scatter plot.
the y - intercept is (square) and the slope is (square). thus, the equation for the trend line is (y=square x+square).
(type integers or decimals rounded to two decimal places as needed.)

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given \((x_1,y_1)=(30,1070)\) and \((x_2,y_2)=(75,1680)\).
\(m=\frac{1680 - 1070}{75 - 30}=\frac{610}{45}\approx13.56\)

Step2: Find the y - intercept

Use the point - slope form \(y - y_1=m(x - x_1)\). Substitute \(m = 13.56\), \(x_1 = 30\), \(y_1=1070\)
\(y-1070 = 13.56(x - 30)\)
\(y-1070=13.56x-406.8\)
\(y = 13.56x+663.2\)
The y - intercept is \(663.2\) and the slope is \(13.56\).

Step3: Find the elevation after one hour

The equation of the line is \(y = 13.56x+663.2\). When \(x = 60\) (since \(x\) is in minutes, one hour \(= 60\) minutes)
\(y=13.56\times60 + 663.2\)
\(y = 813.6+663.2\)
\(y=1476.8\)

Answer:

The y - intercept is \(663.2\), the slope is \(13.56\), the equation of the trend line is \(y = 13.56x+663.2\), and she will be \(1476.8\) feet above sea level after one hour.