Linear Functions.pptx Explanation of linear function

Linear Functions.pptx Explanation of linear function

• 1.
  Linear Functions
• 2.
  Review If y isproportional to x , then When express y in terms of x , y = ? If y is inversely proportional to x , then When express y in terms of x , y = ?
• 3.
  Review Coordinates P(2,3) X coordinate andY coordinate Q (5, -4) R (-2,3) Graphing proportion and inverse proportion
• 4.
  Linear Functions What isa linear function? It’s a function that can be represented as and are constants and How do we determine whether a function is linear or nonlinear?
• 5.
  o A linearequation in two variables, x and y, is an equation that can be written in the form , where a and b are constants (just numbers). o Likewise, a linear function is a function whose graph is a non-vertical line. o A linear function has a constant rate of change and can be represented by a linear equation in two variables. o A nonlinear function does not have a constant rate of change and its graph is not a line.
• 6.
  o If youlet be the total cost of a 40-yen bottle filled with grams of a drug costing 8-yen per gram, then (Total cost) = (Cost of drug) + (Cost of bottle), o It takes seconds to run 400m at a speed of metres per second Time = Examples
• 7.
  o In therectangle on the right, Point P moves from B to C on side BC. Letting cm be the length of segment BP and cm2 be the area of the DPC 1. in terms of 2. Is a linear function of ? 3. Find value for y when = 0 and value of when = 12 4. Domain of x and domain of y (when point P is at vertices B and C) Examples
• 8.
  Does the tablerepresent a linear or nonlinear function? A linear function has a constant rate of change As x increases by 3, y decreases by 6. The rate of change is constant for both x and y. The function is linear. x 3 6 9 12 y 36 30 24 18 +3 +3 +3 -6 -6 -6
• 9.
  Does the tablerepresent a linear or nonlinear function? A linear function has a constant rate of change As x increases by 2, y increases by different amounts. The rate of change is not constant for both x and y. The function is nonlinear. x 1 3 5 7 y 2 9 20 35 +2 +2 +2 +7 +11 +15
• 10.
  o When thex value goes from 2 to 8 in the linear function , find increase in , increase in and the rate of change, Increase in is 8 – 2 = 6 Increase in Rate of change is Examples
• 11.
  Does the graphrepresent a linear or nonlinear function? Explain. The function is linear. Because the graph is a line. The function is nonlinear. Because the graph is not a line.
• 12.
  Which of thefollowing equations represent linear functions? Explain. A linear function can be written in the form , where m and b are constants (just numbers). You cannot rewrite the equations , , , and in the form . So these equations cannot represent linear functions. You can rewrite the equation as You can rewrite the equation as So these equations represent linear functions. , , , , , and
• 13.
  Does the equationrepresent a linear or nonlinear function? Explain. A linear function can be written in the form . You can rewrite the equation as Equation represents a linear function. You can rewrite the equation as Equation represents a linear function. You cannot rewrite the equation as Equation is a nonlinear function.
• 14.
  Graphs of proportion& linear functions The graph of a linear function is a straight line formed by translating the graph of by the amount in the +ve direction along the y-axis. 𝑦 =2 𝑥+ 3
• 15.
  For the linearfunction , complete the table. Substitute each x and y value in the eqn using values. 𝑦 = 2 𝑥 + 3 3
• 16.
  The graph ofthe linear function is a st line with a slope of a and b. The slope is equal to Y intercept is equal to the constant -3.