Linear relationships STAAR review

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 and the direction it goes (positive or negative).

Front

What is the y-intercept?

Back

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

Front

How do you find the slope between 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 does a positive slope indicate?

Back

A positive slope indicates that as the value of x increases, the value of y also increases, showing a direct relationship.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the value of x increases, the value of y decreases, showing an inverse relationship.

Front

What is the significance of a slope of zero?

Back

A slope of zero indicates a horizontal line, meaning that the value of y remains constant regardless of the value of x.

Front

What is the significance of an undefined slope?

Back

An undefined slope occurs in a vertical line, indicating that the value of x is constant while y can take any value.

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.