The sum of two numbers are 26 and their difference is 8 what is the larger number
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Given coordinates of the endpoints of a line segment (5,-9) and (1,3).
In order to find the equation of perpendicular line, we need to find the slope between given coordinates.
Slope between (5,-9) and (1,3) is :
Slope of the perpendicular line is reciprocal and opposite in sign.
Therefore, slope of the perpendicular line = 1/3.
Now, we need to find the midpoint of the given coordinates.
Let us apply point-slope form of the linear equation:
y-y1 = m(x-x1)
y - (-3) = 1/3 (x - 3)
y +3 = 1/3 x - 1
Subtracting 3 from both sides, we get
y +3-3 = 1/3 x - 1 -3
<h3>y = 1/3 x - 4 .</h3>
<h3>Given</h3>
The values of two houses (in thousands of dollars)
A) the nature of the function, linear or exponential, that can be used to model the value after x years
B) the actual function f(x) that can be used in each case
C) f(25) for each house. Is there a significant difference?
<h3>Solution</h3>A) The oddball numbers give you a clue immediately that the value of house 1 will be best modeled by an exponential function.
The value of house 2 is increasing steadily at 9,000 per year, so is modeled by a linear function.
B) The ratio of values from a given year to the year before for house 1 is
... 294.58/286 = 1.03
A check for other years reveals the same ratio, so the exponential function can be written for house 1 as
... f(x) = 286·1.03^x . . . . . value of house 1
In part A we determined the year-to-year difference in value for house 2 is 9,000. That is the slope of the linear function. Then (in thousands), that function is
... f(x) = 286 +9x . . . . . value of house 2
C) After 25 years, the house values are (in thousands of dollars)
The value of house 1 has more than doubled in the same time that the value of house 2 has increased by about 79%. This is a significant difference.
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An exponential function will always outperform a linear function over a long enough time period.