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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10.
Linear Equations
10.1
Word problems of graphing linear functions
10.2
Rate of change
10.3
Slope equation: m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2- x_1}
10.4
General form: Ax + By + C = 0
10.5
Point-slope form: y−y1=m(x−x1)y - y_1 = m (x - x_1)
10.6
Parallel and perpendicular lines in linear functions
CLEP College Algebra
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