Angelique makes beaded jewelry. The graph below shows the number of beads on varying cord lengths.

Question

Jewelry
A graph has cord length (inches) on the x-axis and number of beads on the y-axis. A line has a regression equation of y = 2.52 x + 1.61.

A necklace contains 88 beads. Based on the information above, which is the best estimate for the cord length?
21 inches
26 inches
34 inches
36 inches

Answer 1

To estimate the cord length for a necklace containing 88 beads using the regression equation provided (y = 2.52x + 1.61), we need to set y (the number of beads) equal to 88 and solve for x (the cord length).

The equation is:

\[ 88 = 2.52x + 1.61 \]

Subtract 1.61 from both sides:

\[ 88 - 1.61 = 2.52x \] \[ 86.39 = 2.52x \]

Now, divide both sides by 2.52 to find x:

\[ x = \frac{86.39}{2.52} \]

Calculating this gives:

\[ x \approx 34.24 \]

Based on the available options (21 inches, 26 inches, 34 inches, 36 inches), the best estimate for the cord length is 34 inches.