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.

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.

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.

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.

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.

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.

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.

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.

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.