Linear equation word problems

Front

What is a linear equation?

Back

A linear equation is an equation that represents 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 steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you write an equation from a word problem?

Back

Identify the quantities involved, assign variables to them, and translate the relationships described in the problem into a mathematical equation.

Front

What is the total cost equation for a service with a flat fee and a variable cost?

Back

The total cost (C) can be expressed as C = flat fee + (variable cost per unit * number of units).

Front

If a service charges $50 plus $8 per mile, how would you express the total cost for m miles?

Back

C = 8m + 50.

Front

How do you determine the number of months in a gym membership if the total cost is known?

Back

Use the equation: total cost = monthly fee * number of months + registration fee, and solve for the number of months.

Front

What is the equation for total cost when using a phone service that charges per minute?

Back

The total cost (c) can be expressed as c = (cost per minute * number of minutes) + monthly service fee.

Front

How do you solve for a variable in a linear equation?

Back

Isolate the variable on one side of the equation using inverse operations to solve for its value.

Front

What is the significance of the constant term in a linear equation?

Back

The constant term represents the fixed amount that does not change with the variable, often the starting point or initial value.