Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by the equation y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSF-LE.A.1B

Front

What does the slope of a line represent?

Back

The slope of a line 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 unit change in x.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept in a linear equation?

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

How do you calculate the slope from two points (x1, y1) and (x2, y2)?

Back

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

Tags

CCSS.8.EE.B.5

Front

What is the equation of a line with a slope of 3 and a y-intercept of 2?

Back

The equation of the line is y = 3x + 2.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

If a car travels 104 miles on 4 gallons of gas, what is the rate of change (m)?

Back

The rate of change (m) is 26 miles/gallon.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the slope of the line represented by the equation y = 2x + 6?

Back

The slope of the line is 2.

Tags

CCSS.8.EE.B.5

Front

If Taylor swims 210 meters in 3 minutes, what is the slope of the line when minutes are on the x-axis and meters on the y-axis?

Back

The slope is 70 meters/minute.

Tags

CCSS.8.EE.B.5

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in the y-value as x changes.

Tags

CCSS.8.EE.B.5

Front

What is the initial value when the equation is y = 4x + 5?

Back

The initial value (y-intercept) is 5.

Tags

CCSS.8.EE.B.5