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.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable with respect to the independent variable.

Front

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

Back

m = (y2 - y1) / (x2 - x1) is the formula to calculate the slope.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept represents the value of y when x is 0, indicating where the line crosses the y-axis.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

What is the significance of the point (0, b) in a linear graph?

Back

The point (0, b) is the y-intercept, showing where the line crosses the y-axis.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means the line is horizontal, indicating no change in the dependent variable as the independent variable changes.

Front

What is the formula for finding the y-coordinate given the slope and a point on the line?

Back

Using the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line.