Question

1. use the following data set to perform the tasks in parts a–e.

x	0	3	6	9	12
y	5	28	86	180	310

a. determine an appropriate scale, and plot these points.

Explanation:

Step1: Determine x - axis scale

The x - values are 0, 3, 6, 9, 12. The range of x is \(12 - 0=12\). A scale of 1 unit per grid square for the x - axis is appropriate since the values are evenly spaced (increments of 3) and the maximum x is 12. So we can label the x - axis with 0, 3, 6, 9, 12 at intervals of 3 units (or 1 unit per square, with 3 units between major ticks).

Step2: Determine y - axis scale

The y - values are 5, 28, 86, 180, 310. The range of y is \(310 - 5 = 305\). If we use a scale of 20 units per grid square (or we can also use a scale where we consider the growth rate). Alternatively, since the y - values are increasing and the differences between consecutive y - values are \(28 - 5=23\), \(86 - 28 = 58\), \(180 - 86=94\), \(310 - 180 = 130\), which are increasing. A scale of 20 units per square (or 50 units per square) can be used. Let's choose a scale of 20 units per grid square for the y - axis. So the y - axis will have marks at 0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320.

Step3: Plot the points

• For the point \((0,5)\): Locate \(x = 0\) on the x - axis and \(y=5\) on the y - axis (close to the 0 - 20 mark on the y - axis).
• For the point \((3,28)\): Locate \(x = 3\) on the x - axis and \(y = 28\) (between 20 and 40 on the y - axis).
• For the point \((6,86)\): Locate \(x = 6\) on the x - axis and \(y=86\) (between 80 and 100 on the y - axis).
• For the point \((9,180)\): Locate \(x = 9\) on the x - axis and \(y = 180\) (at the 180 mark on the y - axis).
• For the point \((12,310)\): Locate \(x = 12\) on the x - axis and \(y=310\) (between 300 and 320 on the y - axis).

(Note: Since we can't draw the actual plot here, the description above gives the method to plot the points with an appropriate scale. The x - axis scale can be 1 unit per square (with major ticks at 0, 3, 6, 9, 12) and y - axis scale can be 20 units per square (or other suitable scale based on the data range) and then plot the points \((0,5)\), \((3,28)\), \((6,86)\), \((9,180)\), \((12,310)\) on the coordinate plane.)

Answer:

To plot the points:

• x - axis scale: 1 unit per grid square (major ticks at 0, 3, 6, 9, 12).
• y - axis scale: 20 units per grid square (or a suitable scale based on data range).
• Plotted points: \((0,5)\), \((3,28)\), \((6,86)\), \((9,180)\), \((12,310)\) are plotted on the coordinate plane with the determined scales. (The actual plot would be a set of points on a grid with the x - axis labeled as described and y - axis labeled as described, with each point at the intersection of its x and y values according to the scale.)