Question 3/Multiple Choice Worth 1 points) (02.04 MC) A school system is reducing the amount of dumpster loads of trash removed each week. In week 5, there were 40 dumpster loads of waste removed. In week 10, there were 30 dumpster 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 f(x)=-2x+40 f(x)=2x+40 f(x)=-2x+50 f(x)=2x+50

## Step 1<br />The problem provides two points on the line, (5, 40) and (10, 30). The slope of the line can be calculated using the formula:<br />### \(m = \frac{y_2 - y_1}{x_2 - x_1}\)<br />where \(m\) is the slope, \(x_1\) and \(x_2\) are the x-coordinates of the two points, and \(y_1\) and \(y_2\) are the y-coordinates of the two points.<br /><br />## Step 2<br />Substitute the given points into the formula to calculate the slope:<br />### \(m = \frac{30 - 40}{10 - 5} = -2\)<br /><br />## Step 3<br />The slope of the line is -2, which means the amount of trash removed each week is decreasing by 2 dumpster loads.<br /><br />## Step 4<br />The y-intercept of the line can be calculated using the formula:<br />### \(b = y - mx\)<br />where \(b\) is the y-intercept, \(x\) is the x-coordinate of a point on the line, \(y\) is the y-coordinate of the point, and \(m\) is the slope.<br /><br />## Step 5<br />Substitute the slope and one of the points into the formula to calculate the y-intercept:<br />### \(b = 40 - (-2)*5 = 50\)<br /><br />## Step 6<br />The equation of the line in function form is \(f(x) = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.<br /><br />## Step 7<br />Substitute the slope and y-intercept into the equation to get the final equation:<br />### \(f(x) = -2x + 50\)