Algebraic Relationships

Front

What is an algebraic expression?

Back

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols. For example, 3x + 5 is an algebraic expression.

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What does it mean for one variable to depend on another?

Back

It means that the value of one variable changes in response to the value of another variable. For example, if y depends on x, then as x changes, y will also change.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

Back

The slope of a line is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise over run).

Front

What is the y-intercept?

Back

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

Front

How do you find the value of y in the equation y = 3x?

Back

To find the value of y, substitute a value for x into the equation. For example, if x = 2, then y = 3(2) = 6.

Front

What does the equation y = x + 6 represent?

Back

This equation represents a linear relationship where for every increase of 1 in x, y increases by 1, starting from 6 when x is 0.

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What is a function?

Back

A function is a special relationship where each input (x) has exactly one output (y). For example, f(x) = x + 2 is a function.

Front

What is a table of values?

Back

A table of values is a way to organize pairs of input and output values for a function or equation, showing how the output changes with the input.

Front

What does it mean for two variables to be proportional?

Back

Two variables are proportional if they maintain a constant ratio. For example, if y is proportional to x, then y = kx for some constant k.