Linear Equations 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 (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 steep the line is.

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 is the point where the line crosses the y-axis.

Front

How do you write an equation for a word problem involving a fixed cost and a variable cost?

Back

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

Front

If a taxi charges a flat fee and a per-mile fee, how would you represent the total cost?

Back

Total Cost = Flat Fee + (Per-Mile Fee * Number of Miles).

Front

What is the equation for 'two times a number plus five equals 15'?

Back

2x + 5 = 15.

Front

How do you determine the total cost of an event with an entry fee and additional costs per activity?

Back

Total Cost = Entry Fee + (Cost per Activity * Number of Activities).

Front

What does the variable 'y' typically represent in a linear equation?

Back

In many contexts, 'y' represents the dependent variable, which is the outcome or total cost based on the independent variable 'x'.

Front

How can you convert a word problem into a linear equation?

Back

Identify the quantities involved, determine the relationships between them, and express these relationships using variables and constants.

Front

What is the significance of the coefficients in a linear equation?

Back

Coefficients indicate the relationship between variables; they show how much the dependent variable changes with a one-unit change in the independent variable.