7th Grade - Flashcard - Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the constant of proportionality?

Back

The constant of proportionality is the constant value (k) that relates two proportional quantities. In a proportional relationship, y = kx, where k is the constant of proportionality.

Front

How do you find the slope of a line?

Back

The slope of a line is found by taking the difference in the y-coordinates divided by the difference in the x-coordinates of two points on the line. It is calculated as (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is 0 in the equation y = mx + b.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a relationship to be proportional?

Back

A relationship is proportional if it can be represented by a straight line that passes through the origin (0,0). In a proportional relationship, the ratio of y to x is constant.

Front

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the difference between proportional and non-proportional relationships?

Back

Proportional relationships pass through the origin and have a constant ratio, while non-proportional relationships do not pass through the origin and may have varying ratios.

Front

What does the term 'rate of change' refer to in a linear relationship?

Back

The rate of change refers to how much y changes for a unit change in x. It is represented by the slope (m) in the equation y = mx + b.

Front

How do you interpret the slope of a line in a real-world context?

Back

The slope represents the rate at which one quantity changes in relation to another. For example, in a graph showing distance over time, the slope indicates speed.