chapter 1: functions, graphs, and models; linear functions section 1.4: equations of lines 1
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CHAPTER 1: FUNCTIONS, GRAPHS, AND MODELS; LINEAR FUNCTIONSSection 1.4: Equations of Lines1
SECTION 1.4: EQUATIONS OF LINES
Slope-Intercept Form of the Equation of a Line
y = mx + b where m is the slope, and b is the y-intercept
Point-Slope Form of the Equation of a Liney – y1 = m (x – x1)
where m is the slope, and (x1, y1) is a point on the line.
notice that y and x are not ‘spelled out’ – that is because they are the variables that establish the linear relationship
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SECTION 1.4: EQUATIONS OF LINES
Write equations for each line, given the information provided. slope = 5, y-intercept at (-3, 0)
slope = , passes through (-1, 5)
slope = 0, passes through (-4, 2)
slope is undefined, passes through (-4, 2) 3
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SECTION 1.4: EQUATIONS OF LINES
What happens when the slope = 0? We get a horizontal line in the form y = b.
What happens when the slope is undefined? We get a vertical line in the form x = a.
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SECTION 1.4: EQUATIONS OF LINES
Another form…General Form of the Equation of a Line
ax + by = c where a, b, and c are real numbers. the General Form is a way to express the line
without any fractions.
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SECTION 1.4: EQUATIONS OF LINES
Find the equation of a line that passes through (-1, 5) and (2, 4). Express your answer in slope-intercept form and
general form.
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SECTION 1.4: EQUATIONS OF LINES
The number of people (in millions) in US prisons or jails grew at a constant rate from 1990 to 2000, with 1.1.5 million people incarcerated in 1990 and 1.91 million incarcerated in 2000. Write an equation that models the number of
prisoners, N, as a function of the year, x.
The number of individuals incarcerated in 2005 is projected to be 2.29 million. Does your model agree?
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SECTION 1.4: EQUATIONS OF LINES
For a line, the slope measures the rate of change. However, not every equation is linear. What then? We can measure the Average Rate of Change
The AROC is the slope of the line (called a secant line) connecting two points of interest on the curve.
To find the AROC:
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ab
)a(f)b(f
values x in Change ingCorrespond
values f(x) in ChangeAROC
SECTION 1.4: EQUATIONS OF LINES
The total Toyota hybrid vehicle units sold for the years between 1997 and 2001 can be approximated by the model
S(x) = 2821x3 – 75,653x2 + 674,025x – 1,978,335where x is the number of years after 1990.
Find the average rate of change of total Toyota hybrid sales between 1997 and 1999. Interpret your answer.
What is the relationship between the slope of the secant line joining the points (7,446) and (9,16,506) and your answer? 9
SECTION 1.4: EQUATIONS OF LINES
What happens when real world data isn’t perfectly linear? We can use the AROC to determine a close fitting
line.
The enrollment (in thousands) in grades 9-12 of US schools for the years 1990-2002 is given in the table on the next slide. Create a scatterplot of the data. Find the AROC between 1990 and 2002. Write the equation of the line between 1990 and
2002. Graph your equation with the scatterplot.
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SECTION 1.4: EQUATIONS OF LINES
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Year, x Enrollment, y (in thousands)
1990 12,488
1991 12,703
1992 12,882
1993 13,093
1994 13,376
1995 13,697
1996 14,060
1997 14,272
1998 14,428
1999 14,623
2000 14,802
2001 15,058
2002 15,332
SECTION 1.4: EQUATIONS OF LINES
Homework: pp. 63-69 1-29 every other odd, 31, 33, 35, 37, 41, 45, 51,
53, 55, 59, 65
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