Rate of change

Rate of change

Rate of change is all around us. For example, we express the speed of a car as Kilometer per hour (km/hr), the wage in a fast food restaurant as dollar per hour, and taxi fare as dollar per meter or kilometer. Let's solve some word problems on rate of change.
Basic concepts: Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}, Slope intercept form: y = mx + b, Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1),
Related concepts: Representing patterns in linear relations, Applications of linear equations, Graphing linear inequalities in two variables, Graphing systems of linear inequalities,

Lessons

Rate of change = △y△x=y2−y1x2−x1 {{{\bigtriangleup y} \over {\bigtriangleup x} } = { {y_2 -y_1} \over {x_2 -x_1}}}
Examples: km/hr, miles per gallon, m/s, dollars/hr, etc.
  • 1.
    Draw a graph to describe the fare charged by a taxi with an initial cost of $10.50 plus $2.50 per km traveled.
  • 2.
    Draw a graph to describe the income of a insurance sales person who earns $800 per month plus $400 for every car sold.
  • 3.
    A long distance runner passes the 36 km mark of a race in 1 hr 40 mins, and passes the 44 km mark 1 hr 10 mins later. If the rate is constant, find the speed of the long distance runner in km/hr.
  • 4.
    Cathy hires a super band to play at a wedding. The cost for the wedding was $1000 for the band, plus $50 per guest for food and $3 per guest for beverages. Determine the cost per person if 150 guests attended the wedding, and averaged three drinks per person.
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3.
Linear Functions
3.1
Distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
3.2
Midpoint formula: M=(x1+x22,y1+y22)M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)
3.3
Gradient equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
3.4
Gradient intercept form: y = mx + b
3.5
General form: Ax + By + C = 0
3.6
Gradient-point form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
3.7
Rate of change
3.8
Graphing linear functions using table of values
3.9
Graphing linear functions using x- and y-intercepts
3.10
Graphing from slope-intercept form y=mx+b
3.11
Graphing linear functions using a single point and gradient
3.12
Word problems of graphing linear functions
3.13
Parallel and perpendicular lines in linear functions
3.14
Applications of linear relations
AU Maths Methods
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