Linear Functions
¨A linear function is any function that graphs to a straight line. What this means mathematically is that the function has either one or two variables with no exponents or powers. If the function has more variables, the variables must be constants or known variables for the function to remain a linear function.¨
Parent Functions
The linear parent function is the most basic form of a linear function. The equation of a linear parent function is a line, which makes the equation y=x. A linear parent function has the following characteristics:
Slope: 1 X value increases by 1 Y value increases by 1 Domain: All real numbers Range: All real numbers Y intercept: (0,0) |
The standard form of a linear parent function is f(x) = x. This form can be used while graphing like shown below.
Point slope form:
y - y1 = m(x - x1). To graph in point slope form, it is often easier to make the equation into slope intercept form first and then convert it. Below is an example equation.
y - y1 = m(x - x1). To graph in point slope form, it is often easier to make the equation into slope intercept form first and then convert it. Below is an example equation.
Slope intercept form:
y=mx+b where m is the slope and b is the y intercept which remains constant and where the line crosses the y axis. Shown below is the process of converting from standard form to slope intercept form.
y=mx+b where m is the slope and b is the y intercept which remains constant and where the line crosses the y axis. Shown below is the process of converting from standard form to slope intercept form.
The slope of a linear function in the equation y=a+bx is b. The slope is the change in y over the change over x, or the change in rise over run.
Types of lines:
Horizontal
Types of lines:
Horizontal
Vertical:
Perpendicular:
Parallel:
Inequalities: