Linear Equations

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 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 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 find the initial value in a linear equation?

Back

The initial value is the y-intercept (b) in the equation y = mx + b. It represents the starting point of the relationship.

Front

What is the unit rate?

Back

The unit rate is the ratio of two measurements in which the second measurement is 1. It is often used to express how much of one quantity corresponds to one unit of another quantity.

Front

How do you calculate the unit rate from a total amount?

Back

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

Front

What is the formula for calculating the rate of change?

Back

The rate of change can be calculated using the formula: (change in y) / (change in x). It shows how much y changes for a given change in x.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How can you determine if a linear equation is proportional?

Back

A linear equation is proportional if it passes through the origin (0,0), meaning the y-intercept (b) is 0.