Graphing Linear Equations

Front

What is a function in mathematical terms?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the graph of the equation crosses the y-axis, represented by the value of y when x = 0.

Front

In the equation y = mx + b, what do 'm' and 'b' represent?

Back

'm' represents the slope of the line, and 'b' represents the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does the ordered pair (x, y) represent in a function?

Back

The ordered pair (x, y) represents a specific point on the graph of the function, where 'x' is the input and 'y' is the output.

Front

What is a vertical line and how is it represented in an equation?

Back

A vertical line is a line that goes straight up and down and is represented by an equation of the form x = a, where 'a' is a constant.

Front

How do you find the slope from two points on a line?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the direction and steepness of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.