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 expressed in the form of an equation, typically written as 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 in a linear relationship?

Back

The slope of a line represents the rate of change between the two variables. 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 write the equation of a line given a slope and a y-intercept?

Back

The equation of a line can be written as y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

If a dance costs $5.00 to enter and snacks are $0.75 each, how can you express the total cost in terms of the number of snacks purchased?

Back

The total cost, y, can be expressed as y = 0.75x + 5, where x is the number of snacks purchased.

Tags

CCSS.6.EE.C.9

Front

What is the equation for a holiday meal that costs $12.50 per person plus a $30 delivery fee?

Back

The equation is y = 12.5x + 30, where y is the total cost and x is the number of people.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How can you represent the relationship between calories burned and flights of stairs climbed?

Back

If a person burns 90 calories after climbing 18 flights of stairs, the relationship can be expressed as c = 5f, where c is calories burned and f is flights climbed.

Tags

CCSS.HSF-LE.A.1B

Front

Sonia has $40 in her lunch account and pays $2 each day. What is the equation representing her account balance?

Back

The equation is y = -2x + 40, where y is the money left in her account and x is the number of days.

Tags

CCSS.6.EE.C.9

Front

What does it mean if a graph of a linear relationship has a negative slope?

Back

A negative slope indicates that as one variable increases, the other variable decreases. This shows an inverse relationship.

Tags

CCSS.8.EE.B.5

Front

How do you determine the total cost of items when given a fixed cost and a variable cost per item?

Back

The total cost can be calculated using the equation y = mx + b, where m is the variable cost per item, x is the number of items, and b is the fixed cost.

Tags

CCSS.HSF.LE.B.5