Represent the relationship shown in the table using words, an equation, and a graph. Then determine whether the relationship is a linear function.
Mountain Climbing
Number
of Hours
Climbing, x
Elevation (ft), y
0
1103
1
1200
2
1297
3
1394
Question content area bottom
Part 1
Represent the relationship using words. Choose the correct answer below.
A.
Starting from a height of 1103
ft, you gain 97
ft each additional hour of climbing.
Your answer is correct.
B.
Starting from a height of 1103
ft, you lose 97
ft each additional hour of climbing.
C.
Starting from a height of 97
ft, you gain 1103
ft each additional hour of climbing.
D.
Starting from a height of 97
ft, you lose 1103
ft each additional hour of climbing.
Part 2
Represent the relationship using an equation.
yequals
enter your response here
(Simplify your answer. Type an expression using x as the variable.)
Part 1: In words:
The correct answer is A. Starting from a height of 1103 ft, you gain 97 ft each additional hour of climbing.
Explanation: The table shows that at 0 hours, the climber is at an elevation of 1103 feet. After each additional hour, the elevation increases by the difference between the subsequent elevations, which is 1200 - 1103 = 97 feet after the first hour, and continues similarly for the second and third hours.
Part 2: Equation:
Given the pattern in the relationship, we can create a linear equation to represent this relationship. To make the pattern into an equation, we need to find the starting point, which is the elevation at 0 hours (y-intercept), and the rate of change per hour (slope).
Starting Elevation (y-intercept) = 1103 feet
Rate of Change (slope) = 97 feet per hour
Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept:
y = 97x + 1103
This equation allows you to find the elevation y after x hours of climbing.
Graph: The graph would be a straight line that passes through the point (0, 1103) and has a slope (rise over run) of 97. Since we're dealing with hours as the independent variable and elevation as the dependent variable, the x-axis would represent the number of hours climbing, and the y-axis would represent the elevation in feet.
To determine whether the relationship is a linear function, you can look at the equation and the graph. Since the equation represents a straight line with a constant rate of change (97 feet per hour), and this would be reflected in the graph as a straight line, the relationship is a linear function.