Arnold's Math Review

Front

What is the formula to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does it mean for a set of values to be a function?

Back

A set of values is a function if each input (x-value) corresponds to exactly one output (y-value).

Front

Find the slope of the line that passes through the points (2, 4) and (6, 12).

Back

Slope = 2

Front

What is an estimate in mathematics?

Back

An estimate is an approximate calculation or judgment of a value.

Front

What is the solution to a system of equations?

Back

The solution is the point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

What does 'no solution' mean in the context of a system of equations?

Back

'No solution' means that the equations represent parallel lines that never intersect.

Front

What is the difference between a linear function and a non-linear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a non-linear function does not.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis (x=0).

Front

How do you determine if a relation is a function from a set of ordered pairs?

Back

Check if any x-value is repeated with a different y-value; if so, it is not a function.

Front

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

Back

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