Final answer:
The correct equation in slope-intercept form that reflects the increasing U.S. consumption of renewable energy between 2002 and 2005 is P = 6.07 + 0.17y, where P is the amount of renewable power produced and y is the year. Therefore, answer A is correct.
Step-by-step explanation:
To write the equation in slope-intercept form to find the amount of renewable power P in quadrillion BTUs produced in year y between 2002 and 2005, we start with the given information that U.S.
consumption of renewable energy increased an average of 0.17 quadrillion BTUs per year and that in the year 2002, about 6.07 quadrillion BTUs of renewable power were produced.
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope (rate of change) and b is the y-intercept (starting value).
In this case, the slope m is the annual increase of renewable energy consumption, which is 0.17, and the y-intercept b is the amount of energy produced in the base year 2002, which is 6.07.
Since we want the equation to reflect the amount of renewable power produced in any given year, we have to set y to P (power produced), and make x correspond to the years after 2002 by using y - 2002.
The correct equation in slope-intercept form would then be P = 6.07 + 0.17(y - 2002).
To simplify, distribute 0.17 to both terms inside the parentheses:
- P = 6.07 + 0.17y - 0.17(2002)
- P = 6.07 + 0.17y - 340.34
- P = -334.27 + 0.17y
However, none of the given options match this simplified form. Looking back at the given options, the equation should still reflect the base year as 2002.
Hence, we want an equation where the slope (0.17) is multiplied with the number of years since 2002, leading us to choose option A which is structured correctly as a slope-intercept with years since 2002 factored into 'y'.
The correct equation, which is represented by the choices given, is A. P = 6.07 + 0.17y.