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, where m is the slope and b is the y-intercept.

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 steep the line is.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined because the change in x is zero, which would involve division by zero.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating that there is no change in the y-value as x changes.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of y when x = 0.

Front

In the equation y = mx + b, what does 'b' represent?

Back

'b' represents the y-intercept of the line.

Front

What is the difference between the slope and the y-intercept?

Back

The slope indicates the steepness and direction of the line, while the y-intercept indicates where the line crosses the y-axis.

Front

If a line has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, the value of y increases by 2 units.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, resulting in a downward slant of the line.