Question

based on the scatter plot, which equation represents a line of best fit that could be used to model the relationship between the weights of the dumbbells and the numbers of repetitions that jessie can perform?
a. ( y = - 0.8x + 30 )
b. ( y = - 1.5x + 50 )
c. ( y = - 2.8x + 73 )
d. ( y = - 3.5x + 52 )

Explanation:

Step1: Identify trend direction

The scatter plot shows a negative correlation (as x increases, y decreases), so the slope is negative (all options satisfy this).

Step2: Estimate y-intercept

The y-intercept is the y-value when x=0. From the plot, when x≈15, y≈28; when x≈20, y≈24. Test x=0 for options:
A: y=30; B: y=50; C: y=73; D: y=52. 30 is the most reasonable estimate.

Step3: Verify slope

Check option A with x=15: y=-0.815+30=18? Wait, no—wait the first point is ~x=15, y≈28. Wait recalculate: -0.815 +30 = -12+30=18? No, wait maybe x=15 is ~28: let's use x=15, y≈28 for option A: 28 vs -0.815+30=18 no, wait x=10 (if x=10 were present): y=-0.810+30=22, which is close to the trend. Option B: x=15, y=-1.515+50=27.5≈28 (matches first point). x=20: -1.520+50=20 (close to plot's ~24? No, option A x=20: -0.820+30=14 (too low). Option B x=20:20, x=25: -1.525+50=12.5 (close to plot's ~10). Option A is too shallow, B is better. Wait wait original plot: first point ~x=15,y≈28: B gives 27.5, which is almost exact. Second point ~x=20,y≈24: B gives 20 (close), third ~x=22,y≈17: B gives -1.5*22+50=17 (exact). Oh right! So B is correct.

Answer:

B. y = -1.5x + 50