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 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 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 equation of a line given a point and the slope?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What does it mean for two items to add to a total in a word problem?

Back

It means that the sum of the values of the two items equals a specific total, which can be represented as a linear equation.

Front

How do you represent a situation where one quantity decreases over time?

Back

Use a linear equation with a negative slope, indicating that as time increases, the quantity decreases.

Front

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

Back

Coefficients represent the relationship between the variables. For example, in y = mx + b, m indicates how much y changes for a unit change in x.

Front

How can you determine the total score from correct and incorrect answers?

Back

Use the equation: Total Score = (Points per correct answer * Number of correct answers) - (Points lost per incorrect answer * Number of incorrect answers).