Solve. Assume the exercise describes a linear relationship. When writing a linear equation, write the equation in
slope-intercept form.
-In 1995 the United States recovered 20% of its municipal wastes through recycling, up from 17% in 1990. Find a linear equation that fits this data. Use this equation to predict the percentage recycled in 2004.
A)21.8%
B)27.1%
C)23.5%
D)25.4%

Question

Quizplus · Accepted Answer

To find the equation of the line, we can use the slope-intercept form:

y = mx + b

where y represents the percentage of municipal waste recycled, x represents the year (with 1990 as x = 0), m represents the slope (rate of change), and b represents the y-intercept (the percentage recycled in 1990).

We can find the slope by subtracting the percentage recycled in 1990 (17%) from the percentage recycled in 1995 (20%), and dividing the result by the number of years between those two points:

m = (20% - 17%) / 5 years = 0.6%

So the equation becomes:

y = 0.6x + 17

To predict the percentage recycled in 2004, we plug in x = 14 (since 1990 is x = 0, 2004 is x = 14):

y = 0.6(14) + 17 = 25.4%

Therefore, the answer is D, 25.4%. To find a linear equation, we need to use the two given data points: (1990, 17) and (1995, 20).

First, we need to find the slope of the line using the formula:

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

Slope = (20 - 17) / (1995 - 1990)
Slope = 0.6

Next, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (1990, 17), we get:

y - 17 = 0.6(x - 1990)

To convert to slope-intercept form, we simplify:

y = 0.6x - 159

Now, we can use this equation to predict the percentage recycled in 2004.

x = 2004
y = 0.6(2004) - 159
y = 25.4%

Therefore, the best answer is D) 25.4%.

Solve Assume the Exercise Describes a Linear Relationship