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 1202
2 1301
3 1400
Represent the relationship using words. Choose the correct answer below.
A. Starting from a height of 1103 ft, you lose 99 ft each additional hour of climbing. B. Starting from a height of 99 ft, you gain 1103 ft each additional hour of climbing. OC. Starting from a height of 1103 ft, you gain 99 ft each additional hour of climbing. OD. Starting from a height of 99 ft, you lose 1103 ft each additional hour of climbing.
Represent the relationship using an equation. y = ___ (Simplify your answer. Type an expression using x as the variable .)
A. Starting from a height of 1103 ft, you gain 99 ft each additional hour of climbing.
Represent the relationship using an equation:
y = 1103 + 99x
The relationship is a linear function because the elevation increases by a constant rate with each additional hour of climbing.
The relationship can be represented using words as: Starting from a height of 1103 ft, you gain 99 ft each additional hour of climbing.
The relationship can be represented using an equation as: y = 1103 + 99x
The relationship is a linear function because the elevation increases by a constant rate (99 ft) for each additional hour of climbing, which corresponds to a linear relationship on a graph.
To represent the relationship shown in the table using words, we can observe that for each additional hour of climbing, the elevation increases by 99 feet. Therefore, the relationship can be represented as:
C. Starting from a height of 1103 ft, you gain 99 ft each additional hour of climbing.
To represent the relationship using an equation, we can write:
y = 1103 + 99x
Here, y represents the elevation (in feet) and x represents the number of hours of climbing.
Next, let's determine whether the relationship is a linear function. We can do this by examining the pattern in the table. In a linear relationship, the values of y should increase or decrease by a constant rate for each increase in x. Looking at the table, we can see that for each additional hour of climbing, the elevation increases by a constant value of 99 feet. Therefore, the relationship is a linear function.
Finally, we can represent the relationship using a graph. We can plot the x-values (number of hours climbing) on the x-axis and the y-values (elevation in feet) on the y-axis. The points (0, 1103), (1, 1202), (2, 1301), and (3, 1400) form a straight line, confirming that the relationship is a linear function.
Please note that to visualize the graph and see the plotted points, a graphing tool or software can be utilized.