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 shows that as one variable changes, the other variable changes at a constant rate.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

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.

Front

How do you write the equation of a line in slope-intercept form?

Back

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

Front

What is the difference between positive and negative slope?

Back

A positive slope means that as x increases, y also increases, resulting in an upward slant. A negative slope means that as x increases, y decreases, resulting in a downward slant.

Front

What is a proportional relationship?

Back

A proportional relationship is a specific type of linear relationship where the line passes through the origin (0,0) and can be expressed as y = kx, where k is a 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 formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning they intersect at a right angle.