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

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 =
`(y_2-y_1)/(x_2-x_1)` =
`(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