Initial Value and Rate of Change

Front

What is the definition of initial value in a linear equation?

Back

The initial value is the y-intercept of the equation, representing the starting point of the dependent variable when the independent variable is zero.

Tags

CCSS.8.EE.B.5

Front

How do you determine the rate of change from a graph?

Back

The rate of change is determined by calculating the slope of the line, which is the change in the y-values divided by the change in the x-values.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What does a negative rate of change indicate in a real-world context?

Back

A negative rate of change indicates a decrease in the quantity being measured over time.

Tags

CCSS.HSF-LE.A.1B

Front

In the equation y = mx + b, what do 'm' and 'b' represent?

Back

'm' represents the rate of change (slope), and 'b' represents the initial value (y-intercept).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

How can you interpret the unit rate in a real-world scenario?

Back

The unit rate provides a comparison of two different quantities, showing how much of one quantity corresponds to one unit of another quantity.

Tags

CCSS.6.RP.A.1

CCSS.6.RP.A.2

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept indicates the value of the dependent variable when the independent variable is zero, providing a starting point for the function.

Tags

CCSS.HSF.LE.B.5

Front

How do you find the unit rate from a table of values?

Back

To find the unit rate, divide the change in the dependent variable by the change in the independent variable, focusing on the value when the independent variable equals one.

Tags

CCSS.HSF-LE.A.1B

Front

What does it mean if the rate of change is constant in a linear relationship?

Back

A constant rate of change means that the relationship between the two variables is linear, and the graph will be a straight line.

Tags

CCSS.HSF-LE.A.1B

Front

How can you express a rate of change in different units?

Back

A rate of change can be expressed in various units by converting the quantities involved, ensuring that the relationship remains consistent.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6