For Exercises 17–22, use the point-slope formula to write an equation of the line given the following information. (See Example 2.) The line passes through the points ( 2.2 , − 3.3 ) and ( 12.2 , − 5.3 ) .
For Exercises 17–22, use the point-slope formula to write an equation of the line given the following information. (See Example 2.) The line passes through the points ( 2.2 , − 3.3 ) and ( 12.2 , − 5.3 ) .
Solution Summary: The author calculates the equation of the line passing through the points using the point-slope formula.
For Exercises 17–22, use the point-slope formula to write an equation of the line given the following information. (See Example 2.)
The line passes through the points
(
2.2
,
−
3.3
)
and
(
12.2
,
−
5.3
)
.
Formula Formula Point-slope equation: The point-slope equation of a line passing through the point (x 1 , y 1 ) with slope m , is given by the following formula: y - y 1 = m x - x 1 Example: The point-slope equation of a line passing through (2, -6) with slope 5 is given by: y - (-6) = 5(x - 2) y + 6 = 5(x - 2)
U.S. Population The number of White non-Hispanicindividuals in the U.S. civilian non-institutional population 16 years and older was 153.1 million in 2000and is projected to be 169.4 million in 2050.(Source: U.S. Census Bureau)a. Find the average annual rate of change in population during the period 2000–2050, with the appropriate units.b. Use the slope from part (a) and the population in2000 to write the equation of the line associatedwith 2000 and 2050.c. What does this model project the population to bein 2020?
World Military Expenditure The following chart shows total military and arms trade expenditure from 2011–2020 (t = 1 represents 2011).
†A bar graph titled "World military expenditure" has a horizontal t-axis labeled "Year since 2010" and a vertical axis labeled "$ (billions)". The bar graph has 10 bars. Each bar is associated with a label and an approximate value as listed below.
1: 1,800 billion dollars
2: 1,775 billion dollars
3: 1,750 billion dollars
4: 1,730 billion dollars
5: 1,760 billion dollars
6: 1,760 billion dollars
7: 1,850 billion dollars
8: 1,900 billion dollars
9: 1,950 billion dollars
10: 1,980 billion dollars
(a)
If you want to model the expenditure figures with a function of the form
f(t) = at2 + bt + c,
would you expect the coefficient a to be positive or negative? Why? HINT [See "Features of a Parabola" in this section.]
We would expect the coefficient to be positive because the curve is concave up.
We would expect the coefficient to be negative because the…
Write the equation for the line through the points (-2, 8)
and (7, –10) in the form y = m(x – xo) + yo where m is the
slope of the line and (xo, yo) is a point that it passes through.
This is sometimes referred to as the point-slope form of the
line.
y =
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