Warm Up (Rate of Change "m" and Initial Value "b")

Front

What does the rate of change 'm' represent in a linear equation?

Back

The rate of change 'm' represents the slope of the line, indicating how much the dependent variable (y) changes for a unit change in the independent variable (x).

Front

What is the initial value 'b' in a linear equation?

Back

The initial value 'b' is the y-intercept of the equation, representing the value of y when x is 0.

Front

How do you determine the rate of change from a real-world scenario?

Back

The rate of change can be determined by identifying how much one quantity changes in relation to another quantity over a specific period.

Front

What is the formula for a linear equation in slope-intercept form?

Back

The formula is y = mx + b, where m is the slope and b is the y-intercept.

Front

In the equation y = 10x + 25, what does the 10 represent?

Back

The 10 represents the rate of change (slope) of the equation, indicating that for every unit increase in x, y increases by 10.

Front

If a graph has a y-intercept of 1, what does this indicate?

Back

This indicates that when x = 0, the value of y is 1.

Front

How can you find the initial value from a given linear equation?

Back

You can find the initial value by identifying the constant term (b) in the equation y = mx + b.

Front

What is the significance of the slope in a real-world context?

Back

The slope indicates the rate at which one quantity changes in relation to another, which can represent speed, cost per unit, or other rates.

Front

What does it mean if the rate of change is negative?

Back

A negative rate of change indicates that as one variable increases, the other variable decreases.

Front

How do you interpret the initial value in a business context?

Back

The initial value can represent fixed costs or starting amounts before any variable costs are added.