Construct Functions to Model Linear Relationships

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

How do you find the slope (m) of a linear function using two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the two points.

Tags

CCSS.8.EE.B.5

Front

What does the y-intercept (b) represent in a linear equation?

Back

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

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant.

Tags

CCSS.7.RP.A.2A

Front

How can you determine if an equation is proportional?

Back

An equation is proportional if it can be written in the form y = kx, where k is a constant.

Tags

CCSS.7.RP.A.2C

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope (m), which represents how much y changes for a unit change in x.

Tags

CCSS.HSF-LE.A.1B

Front

How do you write an equation for a linear function given two ordered pairs?

Back

Use the two ordered pairs to find the slope (m). Then substitute the slope and one ordered pair into y = mx + b to solve for b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the steepness of the line and the direction of the relationship between x and y. A positive slope means y increases as x increases, while a negative slope means y decreases as x increases.

Tags

CCSS.8.EE.B.5

Front

What does it mean for a function to be non-proportional?

Back

A non-proportional function does not have a constant ratio between the variables and cannot be expressed in the form y = kx.

Tags

CCSS.8.EE.B.5