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
0,1,2,3
Elevation (ft), y
1123, 1215, 1307,1399
A. Starting from a height of 92 ft you gain 1123ft each additional hour of climbing.
B. Starting from a height of 92 ft you lose 1123ft each additional hour of climbing.
C. Starting from a height of 1123 ft you lose 92 ft each additional hour of climbing.
D. Starting from a height of 1123 ft you gain 92 ft each additional hour of climbing.
A. Equation: y = 1123x + 92
Graph:
{graph(200,200,-1,4,-200,2000,1123x+92)}
This relationship is a linear function because the equation is in the form y = mx + b, where m is the slope (1123) and b is the y-intercept (92).
Starting from a height of 1123 ft you gain 92 ft each additional hour of climbing.
Represent the relationship using an equation.
y= blank
y = 92x + 1123
Is the relationship a linear function?
No, the relationship is not a linear function because the equation is not in the form y = mx + b, where m is the slope and b is the y-intercept.
To represent the relationship shown in the table, we can use words, an equation, and a graph.
Words: The relationship can be described as "Starting from a height of 1123 ft, the elevation increases by 92 ft for each additional hour of climbing."
Equation: We can represent the relationship using the equation: y = 1123 + 92x, where y represents the elevation (in ft) and x represents the number of hours climbing.
Graph: We can plot the points from the table on a graph, with the x-axis representing the number of hours climbing and the y-axis representing the elevation. Each point represents a pair of values (x, y), where x is from the "Number of Hours Climbing" column and y is from the "Elevation (ft)" column. Then we can connect the points with a straight line.
Now, let's determine whether the relationship is a linear function. A linear function is a function that can be represented by a straight line. In this case, the equation y = 1123 + 92x represents a linear function because it is in the form of y = mx + b, where m is the slope (92) and b is the y-intercept (1123).
Therefore, the answer is D. Starting from a height of 1123 ft, you gain 92 ft each additional hour of climbing. The relationship is a linear function.