Question

The corresponding data for electricity generated by hydropower are 248 million megawatt hours in 2007 and 277 million megawatt hours in 2012. Write a linear model that represents the number of megawatt hours generated by hydropower as a function of the number of years since 2007.

Answer 1

A linear model can be represented by the equation y = mx + b, where y is the dependent variable (megawatt hours generated by hydropower), x is the independent variable (years since 2007), m is the slope of the line, and b is the y-intercept.

To find the slope (m) and y-intercept (b) for this problem, we can use the two points given: (2007, 248) and (2012, 277).

m = (277 - 248) / (2012 - 2007) = 29 / 5 = 5.8

b = 248 - (5.8)(2007) = 248 - 11456 = -11208

So the linear model representing the number of megawatt hours generated by hydropower as a function of the number of years since 2007 is:

y = 5.8x - 11208

where x is the number of years since 2007.

Answer 2

A linear model representing hydropower generation in megawatt hours as a function of the number of years since 2007 is y = 5.8x + 248, where y is the number of million megawatt hours generated, and x is the number of years since 2007.

Step-by-step explanation:

To write a linear model that represents the number of megawatt hours generated by hydropower as a function of the number of years since 2007, we need to find the slope of the line that passes through the points (0, 248) and (5, 277), where the x-values represent the number of years since 2007, and the y-values represent the number of million megawatt hours.

Step 1: Calculate the slope.

The slope (m) is given by the formula:

m = (y2 - y1) / (x2 - x1)

Substituting the given values:

m = (277 - 248) / (5 - 0) = 29 / 5 = 5.8

Step 2: Write the linear equation.

The linear model will have the form y = mx + b, with m representing the slope, and b representing the y-intercept. Since the y-intercept (b) is the output when x is 0, from our data b = 248.

The linear model is therefore:

y = 5.8x + 248

where y is the number of million megawatt hours of electricity generated by hydropower, and x is the number of years since 2007.