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 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 steep the line is and the direction it is going (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 in the equation of the line.

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 about a linear relationship?

Back

A positive slope indicates that as the independent variable (x) increases, the dependent variable (y) also increases, showing a direct relationship.

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What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing an inverse relationship.

Front

What is the difference between a function and a non-function?

Back

A function is a relation where each input (x) has exactly one output (y). A non-function may have one input that corresponds to multiple outputs.

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How can you determine if a relation is a function from a graph?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, the relation is not a function.

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What is the domain of a linear function?

Back

The domain of a linear function is the set of all possible input values (x) for which the function is defined, typically all real numbers.