8th Math Semester 1 Review

Front

What is the definition of a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a graph?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about a graph?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What does a zero slope indicate about a graph?

Back

A zero slope indicates that the line is horizontal, meaning there is no change in y as x changes.

Front

What does an undefined slope indicate about a graph?

Back

An undefined slope indicates that the line is vertical, meaning there is no change in x as y changes.

Front

How do you construct a linear function from a word problem?

Back

Identify the fixed cost and variable cost, then express the total cost as a function of the variable (e.g., y = mx + b).

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does the term 'rate of change' refer to in mathematics?

Back

Rate of change refers to how much one quantity changes in relation to another quantity, often represented as the slope in a linear function.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means that the equations represent the same line, and thus every point on the line is a solution.