Question

the sugar sweet company needs to transport sugar to market. the graph below shows the transporting cost (in dollars) versus the weight of the transported (in tons). use the graph to answer the questions. (a) what is the slope of the line? (b) how much does the cost increase for each ton of sugar being transported? $

Explanation:

Step1: Identify two points on the line

The line passes through (0, 1600) and let's take another point, say when x = 4, y = 1600 + 4slope? Wait, actually, from the graph, when x=0, y=1600 (y-intercept). Let's find another point. Let's see, the line goes from (0,1600) and let's calculate the slope. The formula for slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take (0, 1600) as (x1, y1) and let's find another point. Let's see, when x=4, what's y? Wait, the graph's y-axis: at x=0, y=1600. Let's check the difference. Wait, maybe the slope is calculated as (change in y)/(change in x). Let's see, from x=0 to x=4, how much does y change? Wait, maybe the line has a slope. Wait, the y-intercept is 1600. Let's take two points: (0, 1600) and (4, 1600 + 4slope? Wait, no, let's look at the graph. Wait, the y-axis: 1600, 2000, 2400, 2800, 3200, 3600, 4000. The x-axis: 0,1,2,3,4,5,6,7,8,9. So when x=0, y=1600. Let's take x=4, what's y? Let's see, the line at x=4: from (0,1600) to (4, 1600 + 4slope). Wait, maybe the slope is (2400 - 1600)/(4 - 0)? Wait, no, 2400 - 1600 is 800? Wait, no, 1600 to 2400 is 800, over 4 units? Wait, no, maybe x=4, y= 1600 + 4slope. Wait, maybe the slope is 400? Wait, no, let's calculate properly. Let's take two points: (0, 1600) and (4, 3200)? Wait, no, 1600 to 3200 is 1600 over 4? No, 3200 - 1600 = 1600, x=4 - 0 =4, so slope is 1600/4=400? Wait, no, 1600 divided by 4 is 400? Wait, 4004=1600, so 1600 + 1600=3200 at x=4? Wait, but the graph at x=4, y would be 1600 + 4400=3200? Let's check the graph. The line goes from (0,1600) upwards. So slope is (y2 - y1)/(x2 - x1). Let's take (0, 1600) and (4, 3200). Then slope is (3200 - 1600)/(4 - 0) = 1600/4 = 400? Wait, no, 3200 - 1600 is 1600, divided by 4 is 400? Wait, 400*4=1600, so yes. So slope is 400.

Step2: Calculate the slope

Using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, with (x1, y1) = (0, 1600) and (x2, y2) = (4, 3200) (assuming that at x=4, y=3200? Wait, no, maybe I made a mistake. Wait, the y-axis: 1600, 2000, 2400, 2800, 3200, 3600, 4000. So from x=0 (y=1600) to x=4, how much does y increase? Let's see, the distance between 1600 and 3200 is 1600, over 4 units, so slope is 1600/4=400. So slope is 400.

Step3: For part (b), the cost increase per ton is the slope

Because the slope of the cost vs weight graph represents the rate of change of cost with respect to weight, so the cost increase per ton is the slope, which is 400 dollars per ton.

Answer:

(a):
400