A school system is reducing the amount of dumster loads of trash removed each week. in week 5, there were 40 dumser loads of waste removed. in week 10, there were 30 dumster loads removed. assume that the reduction in the amount of waste each week is linear. write an equation in function form to show the amount of trash removed each week.

Question

Mathematics

Nelson Dickerson

Today, 16:19

A school system is reducing the amount of dumster loads of trash removed each week. in week 5, there were 40 dumser loads of waste removed. in week 10, there were 30 dumster loads removed. assume that the reduction in the amount of waste each week is linear. write an equation in function form to show the amount of trash removed each week.

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Brooklynn Blevins · Answer 1

The weeks and loads of waste removed serve as the x and y coordinates in the equation you're looking for. Using the coordinates, you can find the slope of the line and then use that slope along with ONE of the coordinates to solve for b, the y-intercept. Use the general linear formula: y = mx + b, where m is the slope and b is the y-intercept. Using the coordinates find the slope:y2 - y1/x2 - x1. Our particular coordinates look like this in that formula: 30-40/10-5 is a slope of - 2. Now that we have the slope, use one of the coordinates to solve for b, the y intercept: 30 = - 2 (10) + b. That is subbing in the x value and the y value of one of the coordinates into the linear form of the equation, leaving us to solve for b. 30 = - 20 + b and b = 50. So filling that in along with our slope gives us a line of y = - 2x + 50. And that's the equation.