The graph shows the prices of different numbers of bushels of corn at a store in the current year. the table shows the prices of different numbers of bushels of corn at the same store for the previous year. a graph shows number of bushels on x-axis and price of corn in dollars on y-axis. the x-axis scale is shown from 0 to 14 at increments of 2, and the y-axis scale is shown from 0 to 98 at increments of 14. a straight line joins the ordered pairs 2, 14 and 4, 28 and 6, 42 and 8, 56 and 10, 70 and 12, 84. previous year number of bushels price of corn (dollars) 2 10 4 20 6 30 8 40 part a: describe in words how you can find the rate of change of a bushel of corn in the current year, and find the value. (5 points) part b: how many dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year? show your work. (5 points)

Number 1:

PART A

We can find the rate of change by simply computing for the slope of the line. The graph you described is linear therefore we can take any points of the line. For the current year let's take the ordered pairs (2,16) and (4,32):

\frac{32-16}{4-2}= \frac{16}{2} =8

Therefore the rate of change for the current year is 8.

PART B

To compare how much the price of a bushel of corn in the current year differ than that of the previous year, we just have to calculate the rate of change for the previous year since this is also giving us the price of one bushel.

We take the ordered pairs (2,12) and (4,24):

\frac{24-12}{4-2} = \frac{12}{2}=6

The rate of change for the previous year is 6. Comparing this with the rate in the current year, we can see that the price has increased by $2.

Number 2:

PART A

We can get the rate of change by getting the slope of the graph. We are free to use any point since the graph being described is linear. We use the ordered pairs (0,100) and (3,40):

\frac{40-100}{3-0}= \frac{-60}{3}=-20

The rate of change is therefore -20. This tells us that for every week that passes, the number of songs Gina has yet to download is reduced by 20.

The initial value meanwhile is just the y value of the first ordered pair which is 100. This just represents the number of songs Gina has to download initially.

PART B

The equation in slope-intercept form has the structure y = mx+b where m is the slope and b is the y-intercept. In our case, m is just the rate of change we computed and b is the initial value. We just substitute these values to the form:

EQUATION: y=-20x+100

Number 3:

PART A

Since the graph described will form a straight line, the concept of similar triangles can be used when comparing the slopes on AB and AC. We just imagine a triangle formed by the line segments and their corresponding x and y components. We can notice that their angles don't actually change so we know that the two triangles formed are proportional. This would mean that getting the slope (Δy/Δx) would yield us the same number.

PART B

The initial value of the graph is 60 meters and this represents the initial position of the shark (it is located 60 meters below the ocean surface).

The slope of the graph is  \frac{100-60}{1-0} =40 and this represents how fast (speed) the shark can dive. We know this because dividing meters over the number of minutes would give us meters/minute and this is describing the speed.

Number 4:

The graph being described in the question looks like the one in the attachment.

PART A

A linear graph is described to have a uniform slope. Looking at the graph, we can see that the line increases, flattens, and decreases again. Because of this we know that it changes slope for these three different lines.

Therefore, we can say that the graph is nonlinear.

PART B

We can tell which part of the graph is increasing by looking at the slope which is positive. In this case it would be line segment K since you can see that its y value started from 0 and ended in 9.

For the constant segment, we look at the line with slope of zero. This would then be the line segment L since its y value started and ended with 9. It did not change at all.

Lastly, for the decreasing segment, we'll look at the line with the negative slope. This would be line segment M since we can see that its y value started from 9 and ended at zero.

ANSWERS: Increasing: K, Constant: L, Decreasing: M (refer to graph)

PART C

We can say that the ant started walking away from the hole for two seconds before stopping when it is 9cm away from it. The ant then stayed at the same spot for three seconds before going back to the hole in two seconds.

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i could probably can you me with a question of mine?

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maybe - definition of supplementary angles. im not sure. sorry

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