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Linear Equations - Word Problems

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Questions and Answers

What does the slope of -3/10 indicate in the context of windchill calculations?

Windchill increases by 3 degrees Fahrenheit for every 10 mph increase in windspeed.

Windchill remains constant regardless of the windspeed.

Windchill decreases by 10 degrees Fahrenheit for every 3 mph increase in windspeed.

Windchill decreases by 3 degrees Fahrenheit for every 10 mph increase in windspeed. (correct)

What is the first step in calculating the linear equation for windchill?

Finding the slope using two data points. (correct)

Calculating windchill for a specific value.

Interpreting the slope.

Determining the reasonable range of windspeed.

How is the y-intercept determined in the windchill calculation process?

By averaging the two windspeed values provided.

By setting the slope equal to zero in the model.

By substituting the slope and a data point into the equation y = mx + b. (correct)

By calculating the difference between two y-values.

What windchill value is calculated for a windspeed of 60 mph using the model?

<p>-27°F</p> Signup and view all the answers

What difficulty does the document express regarding the topic of linear equations?

<p>Students find it challenging to apply linear equations in problem solving.</p> Signup and view all the answers

Study Notes

Linear Equations - Word Problems

Windchill Example: Windchill is dependent on windspeed.
Given a windchill of -15°F with 20 mph wind and -24°F with 50 mph wind.
Find the linear model for windchill.
Calculate the slope: m = (-24 - (-15))/(50 - 20) = -9/30 = -3/10
Find the y-intercept (b): Substitute one point into the equation y = mx + b. -15 = (-3/10)(20) + b. Solve for b, which equals -9
Equation: y = -3/10 x - 9
Interpretation of slope: For every 10 mph increase in windspeed, windchill decreases by 3°F. The y-intercept represents the windchill when the windspeed is 0 mph.
Reasonable range: The reasonable range for windspeed could be from 0 to 60 mph.
Find the windchill for 60 mph wind: Substitute x = 60 into y = -3/10 x - 9. y = -27°F.

Additional Information

Quiz on Thursday, covering linear equations.
Office hours for additional help.
Student expressed difficulty with the material.

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Description

Test your understanding of linear equations through real-world word problems related to windchill calculations. This quiz will help reinforce concepts like slope, y-intercept, and creating linear models from given data. Prepare for the upcoming quiz on Thursday and ensure you're comfortable with these essential skills.