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Chapter 7: Functions

# Linear Function

A linear function is an equation of a line. A function is a linear function if and only if its equation can be written in the form y = mx + b. M is the representation of the slope. A slope of a line is the ratio of the change in y to the change in x. If x1 ¹ x2, the slope of the line through (x1, y1) and (x2, y2) is the ratio. Here are some additional properties of the slope:

The slope of a horizontal line (a constant linear function) is 0.

The slope of a vertical line (not a function) is undefined.

Linear Function

B is the y-Intercept. The y-intercept of a function is the y-coordinate of the point at which the graph crosses the y-axis. If the equation of a linear function is in the form y = mx + b, then b is the y – intercept.

There are two other equation forms of a line. They are the slope-intercept form and the point-slope form. The form y = mx + b is called the slope-intercept form of a linear equation in two variables. The slope is m, and the y-intercept is b. The point-slope form of a linear equation with slope m and passing through the point (xi, yl) is y - y1 = m(x - x1).

Here are some additional properties of the equations of the lines:

The graphs of two linear functions are parallel if and only if their slopes are equal.

Two lines with undefined slopes are parallel.

The graphs of two linear functions are perpendicular if and only if the product of their slopes is - 1.

A line with zero slope and a line with undefined slope are perpendicular.

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