Math 103 Section 1.2: Linear Equations and ... - Bruce E. Shapiro
Math 103 Section 1.2: Linear Equations and ... - Bruce E. Shapiro Math 103 Section 1.2: Linear Equations and ... - Bruce E. Shapiro
Application: Linear Interpolation two points on the line: (q, p) = (8, 2.10), (20, 3.30). Price 5.00 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 .50 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Ounces Slope: We know that the price of an 8-ounce cup is $2.10 and the price of a 20-ounce cup is $3.30. So the change in q is $3.30−$2.10 = $1.20 and the change in p is 20oz.−8oz. = 12oz.. So the slope is: m = 3.30−2.10 20−8 = 1.20 12 = .10 Units for the slope m: dollars per ounce 18
Application: Linear Interpolation Slope is $.10 per ounce. How much does the price increase if the size of the cup increases by 4 ounces? Point-slope form: p − 2.10 = .10(q − 8) Slope-intercept form: p = .10q + 1.30. y-intercept is $1.30. Interpretation: The price of a cup of coffee is $1.30 plus ten cents an ounce. 19
- Page 1 and 2: Math 103 Section 1.2: Linear Equati
- Page 3 and 4: x = y x 2 − y = 3 3x − 4y = 6 y
- Page 5 and 6: The shape of the graph of a linear
- Page 7 and 8: x− and y− intercepts of an equa
- Page 9 and 10: Intercepts for the Price-demand equ
- Page 11 and 12: Slope of a line: The slope or steep
- Page 13 and 14: Special forms for linear equations:
- Page 15 and 16: Special forms for linear equations:
- Page 17 and 18: Application: Depreciation. Linear D
- Page 19: Application: Linear Interpolation T
Application: <strong>Linear</strong> Interpolation<br />
two points on the line: (q, p) = (8, 2.10), (20, 3.30).<br />
Price<br />
5.00<br />
4.50<br />
4.00<br />
3.50<br />
3.00<br />
2.50<br />
2.00<br />
1.50<br />
1.00<br />
.50<br />
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Ounces<br />
Slope: We know that the price of an 8-ounce cup is $2.10 <strong>and</strong><br />
the price of a 20-ounce cup is $3.30. So the change in q is<br />
$3.30−$2.10 = $<strong>1.2</strong>0 <strong>and</strong> the change in p is 20oz.−8oz. = 12oz..<br />
So the slope is:<br />
m = 3.30−2.10<br />
20−8<br />
= <strong>1.2</strong>0<br />
12 = .10<br />
Units for the slope m: dollars per ounce<br />
18
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