Writing Linear Equations from 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 a linear equation from a word problem?

Back

Identify the variables, determine the relationship between them, and express that relationship in the form of a linear equation.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

Front

What is the significance of the equation Ax + By = C?

Back

This equation represents a linear relationship between two variables, where A and B are coefficients that determine the slope and intercept.

Front

How do you interpret the coefficients in the equation y = mx + b?

Back

In this equation, m is the slope indicating the steepness of the line, and b is the y-intercept indicating where the line crosses the y-axis.

Front

What is a real-world example of a linear equation?

Back

An example is the cost of renting a car, where the total cost can be expressed as y = 29x + 50, with x being the number of days rented.

Front

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

Back

Identify the quantities involved, assign variables, and express the relationships using mathematical operations to form an equation.