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Labsheet 1.2

The walking rate is the amount that the distance (in meters) for each person is changing as time increases by 1 second. Alana’s walking rate is 1m/sec. As time increases by 1 second, the distance increases by 1 meter.

What is the starting point for each student? This is called the y-intercept. What is the rate of change for each student? This is called the slope. What does the point (6,12) represent? Whose line is it on? Whose line are these points on? (9,9) (5,12) The greater the walking rate, the steeper the line on the graph. (or greater slope)

Alana: d = t or y = 1x + 0 or y = x Gilberto: d = 2t or y = 2x + 0 or y = 2x Leanne: d = 2.5t or y = 2.5x + 0 or y = 2.5x The walking rate is represented as the number that time is multiplied by to get the distance. This is the number in front of the variable. It is called the coefficient.

In the table, for every increase of 1 unit in x, the value of y increases by a constant amount. Each equation is of the form y = mx Which represents a proportional realtionship. The graph of a proportional relationship is a straight line that passes through the origin.

All three relationships between distance walked and time are proportional. They are all of the form d = rt The value of r is the constant of proportionality for each relationship. (slope)

Alana: increases by 1 m Gilberto: increases by 2 m Leanne: increases by 2.5 m In the table it is found as the difference between the values for distance . In the graph it is the steepness of the line. As x increases by 1, y goes up 1 for Alana, 2 for Gilberto, and 2.5 for Leanne.

If t increases by 5 seconds: Increases by 5 meters In a table – As x increases by 5, find the difference in y values. In a graph – the difference in y-coordinates of two points on the line whose difference in x-coordinates is 5.

Walking rates per minute: Alana: 60 m/min Gilberto: 120 m/min (walking rate per sec x 60 sec) Alana: 60 m/min Gilberto: 120 m/min Leanne: 150 m/min Walking rates per hour: (walking rate per min x 60 min) Alana: 3,600 m/min Gilberto: 7,200 m/min Leanne: 9,000 m/min

George = No Elizabeth = Yes! Constant rate 3m/2s Billie = Yes! Constant rate 2.25 m/s Bob = No