Constructing Linear Functions: Finding Initial Value and Rate of Change

This lesson teaches how to construct linear functions by solving for unknowns. It covers the components of a linear function, such as initial value and rate of change, and how to use these to form equations. The video explains how to analyze graphs to find these values and construct equations using known points, a single point with a rate of change, or two points. The lesson emphasizes understanding the relationship between input and output changes to determine the slope and y-intercept, ultimately forming the equation of a line.

What does the 'm' represent in the equation y = mx + b?

• The initial value

• The slope or rate of change

• The y-intercept

• The x-intercept

If the input increases by 2 and the output decreases by 4, what is the rate of change?

• -4

• -2

• 4

• 2

Given an initial value of 5 and a slope of 3, what is the equation of the line?

• y = 5x + 3

• y = 5x - 3

• y = 3x + 5

• y = 3x - 5

How can you determine the initial value if you know the rate of change and a point on the graph?

• By using the midpoint formula

• By finding the x-intercept

• By using the slope formula

• By calculating the y-intercept

What is the initial value if the line crosses the y-axis at 1?

• 0

• 1

• 2

• 3

When given two points, how do you calculate the rate of change?

• By multiplying the input and output

• By dividing the change in input by the change in output

• By adding the input and output

• By dividing the change in output by the change in input

If the rate of change is -1/2 and the y-intercept is 3, what is the equation of the line?

• y = 1/2x - 3

• y = 1/2x + 3

• y = -1/2x + 3

• y = -1/2x - 3