Proportional Relationships and Functions

These flashcards cover key concepts related to proportional relationships and functions, including slope, intercepts, and definitions pertinent to understanding linear equations.

What is the slope-intercept form of a linear equation?

y = mx + b, where m is the slope and b is the y-intercept.

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Use the formula m = (y2 - y1) / (x2 - x1).

What defines a proportional relationship?

A relationship where there is a constant rate of change between x and y.

What is the constant of proportionality in the equation y = kx?

'k' represents the constant of proportionality, equal to the slope.

What do you need to check for when determining if a set of ordered pairs represents a function?

Each x-value must correspond to exactly one y-value; check for repeating x-values.

What is the vertical line test used for?

To determine if a graph represents a function; it must pass if any vertical line touches the graph at only one point.

What is the significance of the point of intersection in a graph of two linear equations?

It represents the values of x and y that are a solution to both equations.

What indicates a positive slope in a graph?

The line increases from left to right.

What is a coefficient in an algebraic expression?

The number in front of a variable that is multiplying it.

What does a horizontal line represent regarding slope?

A zero slope, indicating no change in y as x changes.

Define a non-proportional relationship in terms of an equation.

An equation that includes addition or subtraction and is not in the form y = kx.

Explain the term 'rate of change' as it relates to slope.

It refers to the ratio of the rise over the run between two points on a graph.

What does 'y varies directly with x' imply about the relationship?

It indicates a proportional relationship where y = kx.

What is a variable in algebra?

A letter used to represent an unknown value.

How can you check your answer when solving an equation?

By plugging it back into the original equation to see if both sides are equal.

What does it mean if a graph has a slope of undefined?

It represents a vertical line where there is no change in x.