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, 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 much y changes for a unit change in x.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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

What does it mean if the slope of a line is 0?

Back

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

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship between the two variables.

Front

How can you determine the equation of a line from a graph?

Back

To determine the equation of a line from a graph, identify the slope and the y-intercept, then use the slope-intercept form y = mx + b.

Front

What is the initial value in a linear relationship?

Back

The initial value in a linear relationship is the value of the dependent variable (y) when the independent variable (x) is 0, which corresponds to the y-intercept.