Question

At an aunt's wedding , Nicolas collected data about an ice sculpture that was about to completely melt . A graph of his data is shown at right . a . Write an equation for a line of best fit . What are the units for the slope and y-intercept in the equation ? b Based on your equation , how tall was the ice sculpture one hour before Nicolas started measuring ?

Answer 1

Answer:

Step-by-step explanation:

From the scatter plot given in the attachment,

a). Line of best fit will pass through two points (0, 10) and (4, 0)

   Let the equation of the line is,

   y = mx + b

   m = slope of the line

   b = y-intercept

   Slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

   m = $\frac{y_2-y_1}{x_2-x_1}$ = $\frac{10-0}{0-4}$

   m = -2.5 inches per hour

   y-intercept = 10 inches

   Therefore, equation of the line will be, y = -2.5x + 10

b). Since, Nicolas started measuring the height of the ice sculpture at x = 0

    One hour before the start of the observations means x = (0 - 1) = -1

    From the given equation,

    y = -2.5(-1) + 10

       = 2.5 + 10

       = 12.5 inch