Elizabeth& Valarie - Linear Function

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Elizabeth& Valarie - Linear Function

  1. 1. Linear FunctionsBy: Elizabeth A. and Valarie P.
  2. 2. 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.
  3. 3. Examples:• Graph 5x-2y=10• Solution
  4. 4. Examples (cont.)• Let x= 0.5(0)-2y= 10 • Let x= 0will give us• -2y= 10 the y-intercept• Y= -5 • Solve for y• (0,-5)
  5. 5. Examples (cont.)• Let y= 0.5x-2(0)= 10 • Let y= 0 will give us• 5x= 10 the x-intercept• X= 2• (2,0)
  6. 6. Examples (cont.)• Let x= 4.5(4)-2y= 10 • 3rd point is a check• 20-2y= 10 • These points would• -2y= -10 be plotted and a line• Y= 5 drawn through them to complete the• (4,5) graph.
  7. 7. Pictures
  8. 8. 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.
  9. 9. 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:
  10. 10. 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.
  11. 11. The end…

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