1. Section 8-3 Chapter 1 Equations of Lines and Linear Models
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2. Equations of Lines and Linear Models
Point-Slope Form
Slope-Intercept Form
Summary of Forms and Linear Equations
Linear Models
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Point-Slope Form
The equation of the line through (x1, y1) with slope m is written in point-slope form as
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4. Example: Finding an Equation Given the Slope and a Point
Find the standard form of an equation of the line with slope 1/3, passing through the point (–3, 2).
Solution
Multiply by 3
Standard form
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5. Example: Finding an Equation Given Two Points
Find the standard form of an equation of the line with passing through the points (2, 1) and (–1, 3).
Solution
Find the slope.
Use either point in the form.
Standard form
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Slope-Intercept Form
The equation of the line with slope m and y-intercept (0, b) is written in slope-intercept form as
Slope
y-intercept
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7. Example: Graphing Using Slope and the y-Intercept
Graph the line with equation
Solution y
Plot the intercept (0, –2) and use the slope: rise 3, run 2.
run 2 x
rise 3
(0, –2)
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8. Summary of Forms of Linear Equations
Standard form
Vertical line
Horizontal line
Slope-intercept form
Point-Slope form
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Linear Models
Earlier examples gave equations that described real data. The process of writing an equation to fit a graph is called curve-fitting. The next example illustrates this concept for a straight line. The resulting equation is called a linear model.
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10. Example: Modeling Costs
Estimates for Medical costs (in billions of dollars) are shown below.
Year
Cost (in billions)
2000
225
2001
243
2002
261
2003
279
2004
297
a) Find a linear equation that models the data.
b) Use the model to predict the costs in 2010.
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11. Example: Medical Costs
Solution
Let x = 0 correspond to 2000, x = 1 correspond to 2001, and so on. We can express the data as ordered pairs:
(0, 225), (1, 243), (2, 261), (3, 279), and (4, 297).
a) To find a linear equation through the data we choose two points to get the slope. Using (0, 225) and (3, 279):
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12. Example: Medical Costs
Solution (continued)
Now since we have the y-intercept (0, 225) we have the equation
b) The value x = 10 corresponds to the year When x = 10,
The model predicts that the costs will be $405 billion in 2010.
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