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.

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 point where the line crosses the y-axis.

Front

How do you determine if a relationship is proportional?

Back

A relationship is proportional if it can be expressed as y = kx, where k is a constant. The graph of a proportional relationship passes through the origin (0,0).

Front

What is the slope of a line?

Back

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

Front

How can 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 difference between a linear and a nonlinear relationship?

Back

A linear relationship can be represented by a straight line, while a nonlinear relationship cannot and may form curves or other shapes on a graph.

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.

Front

What does it mean if a table of values is non-proportional?

Back

If a table of values is non-proportional, it means that the ratio of y to x is not constant, and the graph does not pass through the origin.

Front

How do you identify the y-intercept from a linear equation?

Back

The y-intercept can be identified as the value of y when x = 0 in the equation y = mx + b.