Example 5: Taro and Jiro climbed a mountain and hiked back down. At the suminit and at every station along the way back down, they recorded their altitude and the amount of time they had been travelling. Hiking Data Time Traveled (in minutes) Altitude (in meters) 0 3776 3600 29 3 Å 126 3020 2700 179 3 231 2390 Construct a linear function to model the relationship between Taro's and Jiro's altitude in terms of the amount of time they traveled.

A linear function is an algebraic equation with variables with a degree of only 1 and constants and is represented in a straight line form on a graph.

What is Slope?

The slope Of a straight line (which represents a linear function) is the tangent of the angle made by the line with the x-axis. For a straight line passing through (x1,y1) and (x2,y2) the slope is given by

m= (y2-y1)/(x2-x1).

How to write an equation of a Straight line?

y-y1 = m(x-x1) where y represents y co-ordinate and x represents x- co-ordinate and m is the slope of the line which passes through(x1,y1).

Solving the question with the Above concepts

So let time in minutes be represented by 'x'

So let altitude in meters be represented by 'y'

So the (x,y) coordinates according to the given data are (0,3776),(88/3,3600),(126,3020),(538/3,2700) and (231,2390).

So for slope which is m = (3600-3776)/(88/3-0) so slope = -6.

So the linear function is: y-3776 = -6(x-0)

6x+y=3776

So the linear function for the altitude in terms of the time they traveled is 6x+y = 3776

For more information about straight-line refer to https://brainly.com/question/15602982

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