Linear relationship word problems

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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear equation?

Back

The slope (m) 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.

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 starting point of the linear relationship on the y-axis.

Front

How do you write an equation for a linear relationship given a starting value and a rate of change?

Back

The equation can be written in the form y = mx + b, where m is the rate of change and b is the starting value.

Front

If Jacob has 6 hats and collects 2 hats a week, how can we express the total number of hats he has after x weeks?

Back

y = 2x + 6

Front

Jerry has $20 and makes $7 per hour. Write an equation for his total earnings after x hours.

Back

y = 7x + 20

Front

At Joe's Clown Car Rental, if renting a car costs $35 plus $0.75 for every mile driven, how is the total cost expressed?

Back

y = 0.75x + 35

Front

A man is climbing down from 100 feet high at a rate of 30 feet per minute. Write the equation for his height after x minutes.

Back

y = 100 - 30x

Front

Speedy Boat Rental charges a $15 deposit plus $2 for each hour of use. Write an equation for the total cost C to rent the boat for h hours.

Back

C = 2h + 15

Front

What is the formula to find the total cost when given a fixed fee and a variable cost per unit?

Back

Total Cost = Fixed Fee + (Variable Cost per Unit * Number of Units)