Linear equation word problems

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope in a linear equation represent?

Back

The slope 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.

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 an equation from a word problem involving a flat fee and a variable cost?

Back

Identify the fixed cost (flat fee) and the variable cost (cost per unit). The equation will be in the form: Total Cost = Fixed Cost + (Variable Cost per Unit * Number of Units).

Front

Write the equation for a service that charges a flat fee of $50 plus $8 per mile.

Back

C = 8m + 50

Front

How do you represent a situation where a quantity increases by a constant amount over time?

Back

Use the equation y = mx + b, where m is the constant increase per time unit, and b is the initial quantity.

Front

Write the equation for a fitness club that starts with 80 members and increases by 15 members each month.

Back

y = 15x + 80

Front

How do you find the point where two linear equations are equal?

Back

Set the two equations equal to each other and solve for the variable to find the point of intersection.

Front

If Joe’s Canoes charges $20 plus $4 per hour, how do you write the equation for total cost?

Back

C = 4h + 20

Front

What is the equation for a service with a startup fee and a monthly fee?

Back

y = monthly fee * x + startup fee.