Question

which is the best estimate of the number of beads on a cord that is 16 inches long? jewelry (chart with x-axis cord length (in) and y-axis number of beads)

Explanation:

Step1: Analyze the graph's trend

The graph shows a linear relationship between cord length (x) and number of beads (y). Let's find the slope (rate of beads per inch). Take two points, e.g., (8,24) and (24,72). Slope $m = \frac{72 - 24}{24 - 8} = \frac{48}{16} = 3$. So the equation is $y = 3x$ (since it passes through the origin, y-intercept is 0).

Step2: Calculate for x = 16

Substitute x = 16 into $y = 3x$. So $y = 3\times16 = 48$? Wait, but looking at the graph, at x=16, the point is around 48? Wait, no, wait the x-axis: when x=8, y=24; x=16, let's check the graph. Wait the grid: x=8 (8 inches) has y=24. So per inch, 24/8=3 beads per inch. So for 16 inches, 316=48? Wait but looking at the graph, at x=16, the dot is around 48? Wait the x-axis labels: 2,4,6,8,10,12,14,16,18,20,22,24,26. At x=16, the y-value (number of beads) is around 48? Wait no, wait the first point: at x=8, y=24 (so 24 beads at 8 inches: 24/8=3 per inch). So 16 inches: 316=48. Wait but let's check the graph again. The line passes through (8,24), (16,48), (24,72). Yes, so the equation is y=3x. So for x=16, y=48. Wait but wait the graph: at x=16, the plotted point is around 48? Wait the x=16 is between 14 and 18. At x=14, y is around 42? Wait no, maybe my initial point was wrong. Wait let's take (6,24)? Wait no, the first point is at x=8, y=24? Wait the y-axis: 8,16,24,32,40,48,56,64,72,80,88. The x-axis: 2,4,6,8,10,12,14,16,18,20,22,24,26. At x=8 (8 inches), the y is 24 (so 24 beads). At x=16 (16 inches), using the slope: from x=8 to x=16 is 8 inches, so 24 + 24 = 48? Wait yes, because 8 inches:24, 16 inches:24*2=48. So the best estimate is 48? Wait but wait the graph: when x=16, the dot is at y=48? Wait the line goes through (8,24), (16,48), (24,72). So yes, the equation is y=3x. So for x=16, y=48.

Answer:

48