Question

graphing and trendline practice
directions: use the data tables below to create scatter plot graphs with trendlines. steps you should take:

1. identify which variable is \independent\ and which is \dependent\. hint: usually the variable you measure is \dependent\.
2. label the x axis with the independent variable and the y axis with the dependent variable. include the units they were measured in.
3. look at the range of values for each variable. decide what the smallest and largest values on the graph should be for each axis. usually it is a clean round number slightly smaller and larger than the range of values you need. often (but not always), zero is at the origin. label the max and min values on the graph, and figure out how large each of the squares in between is.
4. graph your data. use a small \x\ instead of a dot for each data point so we dont cover them up with our trendline.
5. draw a dashed line or curve that shows the overall trend of the data. it should not connect each data point, and may not even go through any data points! if you are not sure about a trendline, a simpler trendline is better.

mileage data for a hybrid car

distance traveled (miles)	gas used (gallons)
150	4
27	0.5
132	3.5
45	1
80	2
180	5

which mathematical relationship is best represented by the trendline through this data?

Explanation:

Step1: Identify variables

The distance traveled is the independent variable (x - axis) and gas used is the dependent variable (y - axis) since the amount of gas used depends on the distance traveled.

Step2: Determine axis ranges

For distance traveled (x - axis), the minimum value is 10 miles and the maximum is 180 miles. A good range could be 0 - 200 miles. For gas used (y - axis), the minimum is 0 gallons and the maximum is 5 gallons. A good range could be 0 - 6 gallons.

Step3: Plot data points

Plot the points (10,0), (150,4), (27,0.5), (132,3.5), (45,1), (80,2), (180,5) on the graph using 'x' as the data - point marker.

Step4: Draw trendline

Draw a dashed line that best represents the overall trend of the data. As the distance traveled increases, the gas used also increases. The relationship appears to be approximately linear.

The relationship between distance traveled and gas used is a positive linear relationship. As the distance traveled by the hybrid car increases, the amount of gas used also increases in a somewhat linear fashion.

Answer:

The mathematical relationship best represented by the trendline through this data is a positive linear relationship.