Understanding Linear Equations in Elevation

The video tutorial explains how to model Tara's hiking elevation using a linear equation. Starting at 1200 meters, Tara ascends to 1700 meters over four hours, indicating a constant rate of ascent. The tutorial guides viewers through calculating this rate and formulating a linear equation in slope-intercept form, y = mx + b, where m is the slope (125 meters per hour) and b is the initial elevation (1200 meters). The video emphasizes understanding the relationship between time and elevation through this mathematical model.

What was Tara's starting elevation at the beginning of her hike?

• 1000 meters

• 1200 meters

• 1500 meters

• 1700 meters

How long did it take Tara to reach an elevation of 1700 meters?

• 2 hours

• 3 hours

• 4 hours

• 5 hours

What is the formula to calculate the rate of ascent?

• Change in time divided by change in elevation

• Change in elevation divided by change in time

• Initial elevation minus final elevation

• Final elevation plus initial elevation

What is Tara's rate of ascent in meters per hour?

• 100 meters/hour

• 175 meters/hour

• 125 meters/hour

• 150 meters/hour

What is the general form of the linear equation for Tara's elevation?

• y = b + mx

• y = x + mb

• y = b - mx

• y = mx + b

In the equation y = mx + b, what does 'b' represent?

• The rate of change

• The slope of the line

• The y-intercept

• The x-intercept

What is the slope of the line in Tara's elevation equation?

• 125 meters/hour

• 100 meters/hour

• 150 meters/hour

• 175 meters/hour

What does the 'm' in the slope-intercept form represent?

• The initial elevation

• The rate of ascent

• The total time

• The final elevation

Which of the following is an equivalent form of the equation y = 1200 + 125x?

• y = 125x + 1200

• y = 1200x + 125

• y = 125 + 1200x

• y = 1200 - 125x

How can the equation y = 1200 + 125x be interpreted in terms of Tara's hike?

• It shows the total distance traveled.

• It represents the elevation after x hours.

• It calculates the average speed.

• It determines the time taken to reach the peak.