Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when it is 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 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 find the slope from two points on a line?

Back

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

Front

What is the y-intercept of 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 can you determine the initial value in a linear equation context?

Back

The initial value is typically represented by the y-intercept (b) in the equation y = mx + b. It indicates the starting value of y when x is zero.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity.

Front

How do you calculate a unit rate from a given total?

Back

To calculate a unit rate, divide the total amount by the number of units. For example, if someone earns $200 for 8 hours of work, the unit rate is $200 / 8 hours = $25 per hour.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What does it mean for two variables to be directly proportional?

Back

Two variables are directly proportional if they increase or decrease at the same rate, which can be represented by a linear equation with a positive slope.

Front

What is the difference between a positive slope and a negative slope?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.