Topic 4 understanding 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 the equation of a line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a proportional relationship?

Back

A proportional relationship is a specific type of linear relationship that passes through the origin (0,0). In this case, the ratio of the two variables remains constant.

Front

What does the slope of a line represent?

Back

The slope of a line 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 calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of 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

What does it mean if a graph does not pass through the point (0,0)?

Back

If a graph does not pass through the point (0,0), it indicates that the relationship is not proportional, as proportional relationships must pass through the origin.

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

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

Back

A relationship is linear if the differences between the y-values divided by the differences between the x-values (the slope) are constant for all pairs of points.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing an inverse relationship.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, meaning that the dependent variable (y) does not change as the independent variable (x) changes.