Modeling Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a one-unit increase in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

What does a positive correlation indicate in a graph?

Back

A positive correlation indicates that as one variable increases, the other variable also increases. The graph will slope upwards from left to right.

Tags

CCSS.HSF-LE.A.1B

Front

What does a negative correlation indicate in a graph?

Back

A negative correlation indicates that as one variable increases, the other variable decreases. The graph will slope downwards from left to right.

Tags

CCSS.HSF-LE.A.1B

Front

What is the meaning of the slope in the equation y = -2x + 7?

Back

In the equation y = -2x + 7, the slope of -2 means that for each hour of mowing, the mower is predicted to use 2 gallons of gas.

Tags

CCSS.HSF.LE.B.5

Front

How do you determine the correlation from a scatter plot?

Back

To determine the correlation from a scatter plot, observe the direction of the points: if they trend upwards, it's positive; if they trend downwards, it's negative; if they are scattered without a clear trend, there is no correlation.

Tags

CCSS.HSF-LE.A.1B

Front

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

Back

The formula for calculating the slope (m) between two points is m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What does it mean if a graph has no correlation?

Back

If a graph has no correlation, it means there is no predictable relationship between the two variables. The points are scattered randomly.

Tags

CCSS.HSF-LE.A.1B

Front

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

Back

The x-intercept is the value of x when y is 0. It is the point where the line crosses the x-axis.