Businesses: EG – Someone starting a fishing charter business. Their costs might be $5,000 a year in boat and licensing costs, and $150 for fuel and bait every trip that they take. So: Costs = $150 x Trips + $5,000 C = 150t + 5000 Where do we use this in real life? Trips 0 100 200 Cost $5,000 $20,000 $35,000

Weasel Words:

Constant Variable X Axis/value Y Axis/value Linear Y Intercept Gradient Substitute Weasel Words

Quick Joke…………:

Q: What is blue and smells like red paint? Quick Joke…………

Quick Joke…………:

Q: What is blue and smells like red paint? A: Blue paint Quick Joke…………

PowerPoint Presentation:

Let us consider the business of a plumber, who charges a ‘call out’ fee of $60, and then an hourly fee of $100 an hour.

PowerPoint Presentation:

Let us consider the business of a plumber, who charges a ‘call out’ fee of $60, and then an hourly fee of $100 an hour. What is her total fee? We can write this as a rule: Total Fee = 100 x hours + $60 F = 100h + 60

PowerPoint Presentation:

Total Fee = 100 x hours + $60 F = 100h + 60 Y = 100x + 60 (y = total fee and x = hours) X (hours) 1 2 3 4 Y (total fee ) 100 x 1 + 60 = $160 100 x 2 + 60 = $260 100 x 3 + 60 = $360 100 x 4 + 60 = $460

Finding the y – intercept (where the line crosses the y axis):

Y intercept is where x = 0 Strategy 1: Read off graph x = 0 y = $60 Strategy 2: Use the rule y = 100x + 60 (x = 0) y = 100x + 60 y = $60 We often use the letter c for the y intercept. So, in this case c = 60. Finding the y – intercept (where the line crosses the y axis)

Finding the Gradient (slope):

If we know two points, we can find the gradient. We might get the points from the rule, read them off the graph or from a table of values. In this case, lets use the table of values: RULE: Gradient = (y₂ - y₁)/(x₂ - x₁) (x₁, y₁) = 1, 160 (x₂, y₂) = 4, 460 Finding the Gradient (slope) X (hours) 1 2 3 4 Y (total fee $) $160 $260 $360 $460

PowerPoint Presentation:

RULE: Gradient = (y₂ - y₁)/(x₂ - x₁) (x₁, y₁) = 1, 160 (x₂, y₂) = 4, 460 Gradient: = (y₂ - y₁)/(x₂ - x₁) = (460 – 160)/(4 – 1) = 300/3 = 100 We often use the letter m for the gradient, so in this case m = 100

Standard form of the linear (straight line) equation:

y = mx + c (m is gradient, c is y intercept) y = 3x + 50 gradient = 3 and y intercept = 50 Where we found that the gradient was 100 and the y intercept was 60: y = 100x + 60 Standard form of the linear (straight line) equation

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