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 is the slope in a linear equation?

Back

The slope (m) of a linear equation 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

What does the y-intercept represent in a graph?

Back

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

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.

Front

What is the slope of the line represented by the equation y = 4x + 2?

Back

The slope of the line is 4.

Front

What is the y-intercept of the line represented by the equation y = -3x + 5?

Back

The y-intercept of the line is 5.

Front

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

Back

A slope of 0 means that the line is horizontal, indicating that there is no change in y as x changes.

Front

What does a negative slope indicate about a line?

Back

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

Front

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.