Linear equation word problems

Front

What is a linear equation?

Back

A linear equation is an equation that models 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 one-unit increase 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 represents the starting point of the linear relationship on the y-axis.

Front

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

Back

Identify the fixed cost and the variable cost per unit. The equation can be written as y = (variable cost per unit)x + fixed cost.

Front

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

Back

Total cost (C) can be calculated using the formula C = (variable cost per unit) * (number of units) + (flat fee).

Front

How do you determine the total cost for a service that charges a flat fee plus a per-hour rate?

Back

To find the total cost, use the equation C = (per-hour rate) * (number of hours) + (flat fee).

Front

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

Back

Coefficients indicate the relationship between variables. In the equation y = mx + b, m is the coefficient of x and represents the slope, while b is the constant term.

Front

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

Back

This situation can be represented by a linear equation of the form y = mx + b, where m is the constant increase per time unit.

Front

What is the process for solving a linear equation?

Back

To solve a linear equation, isolate the variable on one side of the equation using algebraic operations such as addition, subtraction, multiplication, or division.

Front

How do you interpret the solution of a linear equation in a real-world context?

Back

The solution of a linear equation represents the value of the variable that satisfies the equation, often corresponding to a specific scenario in a real-world application.