Fall Benchmark Review

Front

What is the definition of a function in mathematics?

Back

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

Front

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

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept of a linear function from its graph?

Back

The y-intercept is the point where the graph crosses the y-axis, which occurs when x = 0.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

What is the significance of the coordinates in the solution of a system of equations?

Back

The coordinates represent the point where the two equations intersect, indicating the values of x and y that satisfy both equations.

Front

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

Back

A relation is a function if no two ordered pairs have the same first element (x-value).

Front

What is the process for converting an equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What does it mean for a graph to be linear?

Back

A graph is linear if it forms a straight line, indicating a constant rate of change between the variables.

Front

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

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the relationship between the slope of a line and its angle of inclination?

Back

The slope of a line is equal to the tangent of the angle of inclination that the line makes with the positive x-axis.