Question

A hiker hikes at a steady rate throughout the day on a mountain. Which student wrotr a correct equation to represent the linear relationship shown on the table between X, the number of hours hiked and y, the current altitude of the climber?

Answer 1

The correct equation to represent the linear relationship between the number of hours hiked and the current altitude of the climber is y = -500x + 800.

Step-by-step explanation:

To represent the linear relationship between the number of hours hiked (X) and the current altitude of the climber (y), we need to determine the equation of the line that passes through the given points. From the information provided, we can see that the hiker starts at an altitude of 800 m above sea level (when X is 0) and ends at an altitude of 200 m above sea level (when X is 2). By using the slope-intercept form of a linear equation, we can calculate the equation of the line.

Using the formula, y = mx + b, where m is the slope and b is the y-intercept, we can calculate the slope as the change in altitude divided by the change in time, which is (-800 - 200) / (0 - 2) = -500 m/hour.

Since the hiker's altitude decreases with time, the slope will be negative. Now we can substitute one of the given points and the slope into the equation to find the y-intercept. Let's use the point (0, 800):

800 = -500 * 0 + b

800 = b

Therefore, the equation to represent the linear relationship between X and y is y = -500x + 800.

Answer 2

There is no table provided to reference, but the equation that represents a linear relationship between X and Y is:

y = mx + b

where m is the slope of the line and b is the y-intercept. The equation can also be written as:

y = b + mx

where b is the y-intercept and m is the slope. The equation represents a straight line on a graph, where the slope determines the steepness of the line, and the y-intercept is the point where the line crosses the y-axis. To write the equation for the table of X and Y values, we need to determine the slope and y-intercept from the given data.