Tables, Equations, and Graphs Linear

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 line represent?

Back

The slope of a line represents the rate of change between the two variables. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

How do you determine if a table of values is proportional?

Back

A table of values is proportional if the ratio of y to x is constant for all pairs of values.

Front

What is the unit rate?

Back

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

Front

Write the equation for a situation where a person saves $10 per week starting with $50.

Back

y = 10x + 50, where y is the total savings and x is the number of weeks.

Front

What does it mean for a graph to be linear?

Back

A graph is linear if it forms a straight line, indicating a constant rate of change between the variables.

Front

How can you find the equation of a line from a graph?

Back

To find the equation of a line from a graph, identify the slope (rise over run) and the y-intercept, then use the slope-intercept form y = mx + b.

Front

What is the difference between dependent and independent variables?

Back

The independent variable is the one that is changed or controlled in an experiment (usually x), while the dependent variable is the one that is measured (usually y).

Front

If a graph passes through the origin, what does that indicate about the relationship?

Back

If a graph passes through the origin, it indicates that the relationship is proportional, meaning when one variable is zero, the other is also zero.