Linear Relationships Multiple Representations

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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.

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What does the slope of a line represent?

Back

The slope of a line represents the rate of change between the two variables. It indicates how much y changes for a unit change in x.

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How do you find the rate of change from a table of values?

Back

To find the rate of change from a table, calculate the difference in the y-values divided by the difference in the x-values for two points.

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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

What does the equation y = mx + b represent?

Back

This equation represents a linear function where m is the slope and b is the y-intercept.

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How can you identify a linear equation from a graph?

Back

A linear equation can be identified from a graph if the points form a straight line.

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What is the difference between positive and negative slope?

Back

A positive slope means that as x increases, y also increases. A negative slope means that as x increases, y decreases.

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How do you write an equation from a word problem?

Back

To write an equation from a word problem, identify the variables, determine the relationship between them, and express it in the form of a linear equation.

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What does the term 'rate of change' mean?

Back

The rate of change refers to how much one quantity changes in relation to another quantity. In linear relationships, it is represented by the slope.

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What is a table of values in relation to linear equations?

Back

A table of values lists pairs of x and y values that satisfy a linear equation, showing how y changes as x changes.