finding slope: Use two points and find the slope. Use one of the two points and the slope and write an equation using slope intercept form or point slope form
The table gives the primary energy consumption (trillion Btu) in the United States residential sector, beginning with the year 1999. Predict the primary residential energy consumption in 2006.
Year | Btu
1999 | 6784
2001 | 6879
2002 | 6938
2004 | 7019
You need to consider that x axis is associated with the values representing years and y axis is associated with values representing Btu, hence, you need to use the following slope formula such that:
`m_(AB) = (y_A-y_B)/(x_A-x_B)`
Selecting `A(2002,6938), B(2001,6879)` yields:
`m_(AB) = (6938-6879)/(2002-2001)`
`m_(AB) = 59`
You need to use point slope form of equation since you know a point and the slope, or you may use point point form, selecting two of the given points such that:
point slope form`:y - y_A = m_(AB)(x - x_A)`
point point form: `y - y_A = ((y_A-y_B)/(x_A-x_B))(x - x_A)`
Using the point slope form yields:
`y - 6938 = 59(x - 2002) => y = 59x - 111180`
Notice that the point slope form `y - 6938 = 59(x - 2002` ) may be converted in slope intercept form `y = 59x - 111180` (m=59 represents the slope and -111180 represents y intercept).
Hence, evaluating the slope using two points yields `m_(AB) = 59 ` and evaluating the equation of the line that passes through the given points yields`y - 6938 = 59(x - 2002) ` (point slope form) or `y = 59x - 111180 ` (slope intercept form).
Take year values as x and BTU values as y.
1) to find slope we take the extreme values corresponding to year 1999 and 2004 so that x1=1999, y1=6784, x2=2004 & y2=7019
slope = (y2-y1)/(x2-x1) = (7109-6784)/(2004-1999) = 65
slope = 65 Trillion Btu/Year
2) Using a point and slope method, the equation is: y-y1 = 65(x-x1)
=> y-6784 = 65(x-1999)
=> y = 6784+65(x-1999)
3) To predict primary residential energy consumption in 2006, x=2006
y = 6784+65(2007-1999) = 7239
The primary residential energy consumption in 2006 = 7239 Trillion Btu