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 the y-value with respect to the x-value. It indicates how steep the line is.

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 of 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 equation of a line with a slope of -2 and a y-intercept of 3?

Back

The equation is y = -2x + 3.

Front

If a line has a slope of 0, what does that indicate?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward slant from left to right.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

How can you identify the slope from the equation y = 5x - 4?

Back

The slope is the coefficient of x, which is 5.

Front

What is the slope of the line that passes through the points (1, 2) and (4, 5)?

Back

The slope is (5 - 2) / (4 - 1) = 3 / 3 = 1.