Sure! Let's fill in the boxes to describe what \( m \) and \( b \) represent in real-life situations using a linear function of the form \( y = mx + b \).
In a function
Example for Blank 1:
- \( m \) represents the slope of the line, which is the rate of change. This indicates how much \( y \) changes for a unit change in \( x \).
In a real-life situation:
- Example: In a scenario where \( y \) represents the total cost of gas and \( x \) represents the number of gallons purchased, \( m \) (the slope) would be the price per gallon. If gas costs $3 per gallon, then \( m = 3 \).
Question Blank 1 of 4
Answer:
- \( m \) (slope) represents the rate of change.
image.png (Rate of change)
Example for Blank 2:
- \( b \) represents the y-intercept, which is the value of \( y \) when \( x = 0 \).
In a real-life situation:
- Example: If you have a monthly subscription that costs $10 regardless of usage, then when no months have passed ( \( x = 0 \) ), your total cost \( y \) is $10. Thus, \( b = 10 \).
Question Blank 3 of 4
Answer:
- \( b \) (y-intercept) represents the initial value of \( y \) when \( x = 0 \).
image.png (The y-value of the y-intercept, b)
Example for Blank 4:
- In a savings account where you start with $100 (initial deposit) and you deposit an additional $50 each month, the equation would be \( y = 50x + 100 \); here, \( b = 100 \), the initial deposit.
Question Blank 4 of 4
Answer:
- The y-intercept \( b \) represents the starting value before any changes occur.
This completes the description of \( m \) and \( b \) in both a mathematical and a real-life context.
1 answer