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 variable 'y' represent in a linear function?

Back

In a linear function, 'y' typically represents the dependent variable, which is the output value that depends on the input value 'x'.

Front

What does the slope of 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

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

Back

The equation can be written as y = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed cost.

Front

If a ride costs $2 and entry to the fair costs $10, how would you express the total cost as a function of the number of rides?

Back

The total cost can be expressed as C(x) = 2x + 10, where x is the number of rides.

Front

What is the meaning of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It represents the starting value of the dependent variable.

Front

How can you determine the number of rides Evan can go on if he has a total budget?

Back

You can set up the equation 10 + 2x ≤ total budget and solve for x.

Front

What is the equation to find how much money Sandra has left after x months if she spends $3 each month?

Back

The equation is y = -3x + 20, where y is the amount left after x months.

Front

How do you calculate Norb's total salary based on hours worked and tips received?

Back

Norb's salary can be calculated using the equation S = 4t + 0.95d, where t is hours worked and d is tips.

Front

What does it mean if the slope of a cost function is positive?

Back

A positive slope indicates that as the number of items (or rides) increases, the total cost also increases.