Math96 Section 1.1 The Shape of a Linear Equation
1.1 The Shape of a Linear Equation
Be careful when you are reviewing the data. You may have a table that has a LOT of information, but you may only need a small part. Read the directions in your problem carefully. Read and interpret the data in the table. Do you understand the big picture? The following table is from your text.
What’s BSA mean?
Who are DuBois and Mosteller? And what are there methods?
What’s ml stand for?Can you convert this to ounces?
What’s kg stand for?Can you convert this to pounds?
What’s m2?Can you convert this to square inches?
A Review on Conversions
You are not expected to know conversion facts other than the most common. You will be given the opportunity to look it up online or be given the information.
Usain Bolt, June 2012 ran a 100m race 9.79 sec. Convert this speed to miles per hour.
Make sure you review and study the examples in the text.
Ordered Pairs
Although we talked about ordered pairs in the Introduction lecture, we did emphasize the importance of their “order.” Once the “order” is established, rare is the case when it is reversed. You, as a problem solver, should leave the order as it is given to you.
The order of data pairs is determined by answering the question “what drives what?”
Example: Generally speaking, the number of hours you study will determine the grade you receive. (You could argue the case that your grade will drive how much you study). The point is ORDER MATTERS.
(x,y) – typical representation of a generic ordered pair. In this case “x” is the driver. “x” determines “y”. When graphing, “x” is always the horizontal axis and “y” the vertical. Most of the data we willing be using will be concentrate in the 1st quadrant of the grid.
The first component of the ordered pair is also referred to as the independent variable (in our case above, this would be the x). The second is referred to as the dependent variable (in our case above, this would be the y).
This you must know.
Linear Relationship
Let’s say we have a whole bunch of ordered pairs (a whole bunch of data points), if the independent and dependent variables have a “linear relationship,” what does that mean?
Example?
How will it look on a graph?
Will it be perfect?
From your text: weight vs dosage
The initial data.The initial plot of that data.
If we were to connect the dots, the graph would be pretty close to being a straight line. What we can do is draw in what’s called a “trend line.”Think of it as a line that goes right down the middle of the data where some of the points may actually be on the line. The rest are some points below and some points above . Trend line
Slope, Rise, and Run
When we think of slope, we should be thinking along the lines of “steepness.” Just be careful. You can have a positive steepness, but you can also have a negative steepness.
Given two ordered pairs, slope is the difference in the “y” values divided by the difference in the “x” values. (aka “rate of change”)
Rise/Run
But it’s the units that make sense out of slope.
Example 1.1.1: Calculating slope
Find and interpret the slope for the car value from the table between the years 1998 & 2005.
Solution:
slope =
Meaning: a decrease of approximately $1686 in value for every increase of one year in age.
Note: It does not matter which order you subtract as long as your subtraction starts with x and y from the same point. The other option: slope = . Meaning: an increase of $1686 in value for every decrease of one year in age. Numerically, the slope is -1686 in either case.
The example above is from your text. Pay special attention to the sign of the slope. Generally speaking, the negative is assigned to the numerator.
Graphing Protocol
- independent variable (x) on the horizontal axis
- dependent variable (y) on the vertical axis
- a title
- labels (including units) and a scale for each axis
Homework: Make sure you follow the directions in the text closely. Your graph is to be labeled as stated in the “graphing protocol” (see above and also in the text). Do not put multiple graphs on the same sheet (side).Use a ruler when drawing your axes and trend lines.
For each problem asking for slope: include the set up for finding the slope, your answer before rounding, and your answer after rounding (3 parts).
For each problem asking for the meaning of the slope: answer in a complete sentence using values and units.
Problem 3e, answer in a complete sentence.
Problem 6a, copy and fill in chart.
Problem 6e, answer in a complete sentence.
Problem 10e, answer in a complete sentence.
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