In 1995 the united states recovered 21% of its municiple solid waste through recycling up from 17% in 1990. Let y represent the percentage recycled and let x equal the number of years since 1990. Find the linear function that fits this data.
To find the linear function that fits the data, we need to determine the equation of a line in the form y = mx + b, where y represents the percentage recycled, x represents the number of years since 1990, m is the slope of the line, and b is the y-intercept.
Given that in 1990 (when x = 0), the percentage recycled was 17% (y = 17), and in 1995 (when x = 5), the percentage recycled was 21% (y = 21), we can use these two points to find the equation of the line.
1. Determine the slope (m):
The slope of the line can be found using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Using the points (0, 17) and (5, 21):
m = (21 - 17) / (5 - 0) = 4 / 5 = 0.8
2. Determine the y-intercept (b):
We can substitute the slope value (m = 0.8) and one of the points (5, 21) into the equation y = mx + b and solve for b:
21 = 0.8 * 5 + b
21 = 4 + b
b = 21 - 4 = 17
3. Write the linear function:
Now that we have the slope (m = 0.8) and the y-intercept (b = 17), we can write the linear function as:
y = 0.8x + 17
Therefore, the linear function that fits the data is y = 0.8x + 17.