Comparing Linear Functions

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

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

To find the y-intercept of a linear equation in the form y = mx + b, set x to 0 and solve for y. The value of y when x = 0 is the y-intercept.

A positive slope indicates that as x increases, y also increases. A negative slope indicates that as x increases, y decreases.

To compare the slopes of two linear functions, look at the coefficients of x in their equations. The function with the larger coefficient has a steeper slope.

If two linear functions have the same slope, they are parallel and will never intersect unless they also have the same y-intercept.

The y-intercept of the equation y = 4x + 2 is 2, which is the value of y when x = 0.

To determine which linear function has a greater y-intercept, compare the constant term (b) in the equations of the functions.

The slope of the line represented by the equation y = -3x + 5 is -3.

If two lines intersect, their slopes are different, meaning they are not parallel.