Converting statements involving addition, subtraction, multiplication, and division into linear equations. Here are three examples for each type of statement:
1. Converting an Increased Statement (Use of +) to a Linear Equation:
Statement: "Tom saves $100 more each month." Linear Equation: \(y=100x+b\)
Statement: "The temperature rises by 2 degrees every hour." Linear Equation: \(y=2x+b\)
Statement: "The population of a city grows by 500 people annually." Linear Equation: \(y=500x+b\)
2. Converting a Subtraction Statement (Use of -) to a Linear Equation:
Statement: "Julia's weight decreases by 0.5 kg per week." Linear Equation: \(y=−0.5x+b\)
Statement: "Sales drop by $50 every day." Linear Equation: \(y=−50x+b\)
Statement: "The company's profits decline by 10% each quarter." Linear Equation: \(y=−0.1x+b\)
3. Converting a Product Statement (Use of x) to a Linear Equation:
Statement: "The cost of printing books is $3 per copy." Linear Equation: \(y=3x+b\)
Statement: "A car travels at a speed of 60 km/h." Linear Equation: \(y=60x+b\)
Statement: "A store sells toys for $10 each." Linear Equation: \(y=10x+b\)
4. Converting a Division Statement (Use of /) to a Linear Equation:
Statement: "Susan can read 30 pages in an hour." Linear Equation: \(y=30x+b\)
Statement: "A car consumes 12 liters of fuel per 100 km." Linear Equation: \(y=10012x+b\)
Statement: "It takes 15 minutes to complete one lap on the track." Linear Equation: \(y=115x+b\)
In each example, we've converted statements involving different operations into linear equations of the form \(y=mx+b\), where \(y\) represents the result, \(x\) is the initial quantity, \(m\) represents the rate of change, and \(b\) is an initial value or offset. These linear equations provide a mathematical representation of the given statements, enabling us to analyze and predict relationships between variables in various real-world scenarios.
Facebook
Twitter
Linkedin