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Section 1.4 Formulas for Linear Functions

Section 1.4 Formulas for Linear Functions. Recall from last time…. Linear functions are most commonly written as y = b + mx or y = mx + b where m is the slope and b is the y -intercept where and b gives the value for x = 0 In general

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Section 1.4 Formulas for Linear Functions

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  1. Section 1.4Formulas for Linear Functions

  2. Recall from last time… • Linear functions are most commonly written as y = b + mx or y = mx + b where m is the slope and b is the y-intercept where and b gives the value for x = 0 • In general output = initial value + rate of change x input

  3. Consider the following two linear functions • y = 0.3x + 2 and y = .25x + 4 • What are the slopes and explain their significance • What are the y-intercepts and explain their significance • Will the lines intersect? • What can you say about the graphs of these functions?

  4. Consider the following two linear functions • y = Mx + P and y = Nx + Q where M, P, N and Q represent numbers • Explain the relative positions of the lines (which one is on top of the other) in the following situations • 0 < M < N and P < Q • N < M < 0 and P < Q

  5. Do the following problem in your groups • An empty champagne bottle is tossed from a hot-air balloon. Its upward velocity is measured every second and recorded below • Find a formula for v in terms of t • Explain the significance of the slope in the formula • Explain the physical significance of the t-axis and the v-axis intercepts

  6. Do the following problem in your groups • The stock of company A costs $28 per share and the stock of company B costs $20 per share. You have decided to buy a total of $600 worth of stock in the two companies. Let a be the amount of company A stock and let b be the amount of company B stock. Find a linear function relating the values of a and b. • Interpret the intercepts of this function

  7. Do the following problem in your groups • A hotel finds that if it spends no money on renovations, they will be able to rent 100 rooms per night • They find that for every $5000 spent on renovation, they will be able to rent an additional 25 rooms • If x is the amount of money they spend and y is the number of rooms, find a formula for y as a function of x

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