Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you calculate 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 y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Given the points (-2, 1) and (5, 7), what is the slope?

Back

The slope is 6/7.

Front

What is the slope of the line represented by the equation y = -5/3x + 2?

Back

The slope is -5/3.

Front

If x = 2 in the function y = 3x + 2, what is the value of y?

Back

The value of y is 8.

Front

How do you find the range of the function f(x) = x^2 - 1?

Back

The range is all real numbers greater than or equal to -1, since the minimum value of x^2 is 0.

Front

What does the graph of y = -x + 2 look like?

Back

The graph is a straight line that slopes downwards from left to right, crossing the y-axis at (0, 2) and the x-axis at (2, 0).