Presentation on theme: "Linear Functions By: Elizabeth A. and Valarie P.."— Presentation transcript:
Linear Functions By: Elizabeth A. and Valarie P.
Definition: A function is a linear function if F(X)=ax+b, for real numbers A and B. When a linear function is written in the form Ax+By=C, it is said to be in standard form. The graph of a linear function is a straight line. To graph a linear function, find at least two of its ordered pairs, plot them, and draw a line through them.
This is a picture of the Chapel Bridge in Lucern, Switzerland. The roof of this footbridge, originally constructed in 1333, can be modeled by a linear function. The origin is set at the base of the stone tower. Given this somewhat arbitrary origin, the roof of the bridge could be modeled by the function y = 0.25x + 2.
Review Definition: A linear function is a polynomial of degree one. The graph of a linear function is a straight line. The rate of change of a linear function is called the slope of the function. In a linear function, the average and instantaneous rate of change are always the same. Formula for a Linear Function: General Form: Slope-Intercept Form: Point-Slope Form: Two-Point Form:
Review (cont.) You need only two points to graph a linear function. These points may be chosen as the x and y intercepts of the graph for example. Determine the x intercept, set f(x) = 0 and solve for x. 2x + 4 = 0 x = -2 Determine the y intercept, set x = 0 to find f(0). f(0) = 4 The graph of the above function is a line passing through the points (-2, 0) and (0, 4) as shown below.