Linear FunctionsBy: 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 inLucern, Switzerland.The roof of this footbridge, originally constructed in 1333, can bemodeled by a linear function. The origin is set at the base of thestone tower. Given this somewhat arbitrary origin, the roof of thebridge could be modeled by the function y = 0.25x + 2.
ReviewDefinition:• 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.