5.2 Linear relationships

Weight of objects Create a scatter plot Linear relationship: when the points in a scatter plot lie along a straight line. Is this relationship linear? Yes- the points appear to lie on a straight line. What is the domain? {0,1,2,3,4,5,6,7,8} What is the range? {6.3, 6.5,6.7, 6.9, 7.1, 7.3, 7.5, 7.7, 7.9} Is this relationship proportional? No. The ratio of weight to objects is not constant. Is this relationship a function?yes # of objects Weight (oz)

# of objects Weight (oz) Weight of objects Sometimes it is helpful to connect the points in a scatter plot—especially when you want to make predictions. Find the slope of the line. What are the coordinates of the w-intercept? (0, 6.3) What is the meaning of the w-intercept? This is the weight of the container when there are 0 objects in it.

# of objects Weight (oz) Weight of objects Write an equation that models the weight (w) of the objects and container after (n) objects have been placed in the container. y = mx + b w =.2n Use your table, graph, or equation to predict the weight after 20 objects have been placed in the container. w = 10.3 ounces

Interpreting graphs Linear: As x increases at a constant rate, the function value increases at constant rate Nonlinear: As x increases at a constant rate, the function value changes at varying rates Increasing: Rises from left to right Decreasing Falls from left to right Rate of Change: slope or steepness of a line Continuous: Continuous line Discrete: not a continuous line

Describe the following graphs using the words increasing, decreasing, linear, nonlinear, continuous, discrete, and rate of change Increasing nonlinear continuous Decreasing linear discrete Faster & faster rate of change Constant rate of change

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