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 y = mx + b.

Front

What does 'm' represent in the equation y = mx + b?

Back

'm' represents the slope of the line, which indicates the rate of change of y with respect to x.

Front

What does 'b' represent in the equation y = mx + b?

Back

'b' represents the y-intercept, which is the value of y when x is 0.

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 y divided by the change in x (rise/run).

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship where the ratio of the two variables is constant, and the graph passes through the origin (0,0).

Front

How can you identify a proportional relationship from a graph?

Back

A proportional relationship can be identified if the graph is a straight line that passes through the origin.

Front

What is the constant rate of change?

Back

The constant rate of change is the same as the slope of the line in a linear relationship, indicating how much y changes for a unit change in x.

Front

What is the difference between a proportional relationship and a linear relationship?

Back

All proportional relationships are linear, but not all linear relationships are proportional. A linear relationship may not pass through the origin.

Front

How do you find the slope from 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 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.