Linear functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept (b) in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Front

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

Back

The slope of the line is 3.

Front

What is the y-intercept of the line represented by the equation y = -2x + 4?

Back

The y-intercept of the line is 4.

Front

Identify the slope and y-intercept of the equation y = 1/2x - 3.

Back

Slope: 1/2, Y-intercept: -3.

Front

What does a positive slope indicate about a linear function?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does a negative slope indicate about a linear function?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

What is the formula for finding the y-intercept from a linear equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.