Understanding Linear Equations and Slope

The video tutorial explains how to model the relationship between days and account balance using a linear equation. It starts by analyzing a table showing a constant increase in days and account balance. The tutorial then demonstrates how to formulate a linear equation in the form of y = mx + b, using d and a as variables instead of x and y. It calculates the slope by finding the change in account balance over the change in days and determines the vertical intercept by substituting values from the table. The final equation is a = 25d + 57, indicating the account balance increases by $25 each day, starting with $57.

What is the increase in days as shown in the table?

• 4 days

• 3 days

• 2 days

• 1 day

How much does the account balance increase every three days?

• $100

• $60

• $50

• $75

What form of equation is used to model the relationship between days and account balance?

• Quadratic form

• Slope-intercept form

• Logarithmic form

• Exponential form

In the equation a = md + b, what does 'm' represent?

• The starting amount

• The account balance

• The number of days

• The slope or rate of change

How is the slope calculated using the ordered pairs from the table?

• By dividing the differences

• By subtracting the differences

• By adding the values

• By multiplying the values

What does the slope of 25 indicate in this context?

• The account balance doubles every day

• The account balance decreases by $25 each day

• The account balance remains constant

• The account balance increases by $25 each day

What is the purpose of finding the vertical intercept 'b' in the equation?

• To determine the slope

• To calculate the total days

• To adjust the rate of change

• To find the starting account balance

What is the value of the vertical intercept 'b' in this problem?

• $25

• $50

• $57

• $75

What does the final equation a = 25d + 57 represent?

• The account balance doubles every day

• The account balance decreases by $57 each day

• The account balance increases by $57 each day

• The account balance at day zero is $57

At what day does the account balance start at $57?

• Day 0

• Day 9

• Day 3

• Day 6