Question

which equation best represents the line - of - best fit for the data shown in the table below? \\(\

$$\begin{array}{|c|c|}\\hline x&y\\\\\\hline 3&1\\\\\\hline 4&5\\\\\\hline 5&9\\\\\\hline 7&12\\\\\\hline 8&15\\\\\\hline 10&25\\\\\\hline\\end{array}$$

\\) \\(\bigcirc\\ y = 3x - 8\\) \\(\bigcirc\\ y = 5x - 25\\) \\(\bigcirc\\ y = 4x - 11\\) \\(\bigcirc\\ y = 2x - 3\\)

Explanation:

Step1: Test first point (3,1)

Substitute $x=3$ into each equation:

• $y=3(3)-8=1$ ✔️
• $y=5(3)-25=-10$ ❌
• $y=4(3)-11=1$ ✔️
• $y=2(3)-3=3$ ❌

Step2: Test second point (4,5)

Substitute $x=4$ into remaining equations:

• $y=3(4)-8=4$ (close to 5)
• $y=4(4)-11=5$ ✔️

Step3: Test third point (5,9)

Substitute $x=5$ into remaining equations:

• $y=3(5)-8=7$ (close to 9)
• $y=4(5)-11=9$ ✔️

Step4: Test fourth point (7,12)

Substitute $x=7$ into remaining equations:

• $y=3(7)-8=13$ (very close to 12)
• $y=4(7)-11=17$ (far from 12) ❌

Step5: Verify remaining points

Check $x=8$: $y=3(8)-8=16$ (close to 15)
Check $x=10$: $y=3(10)-8=22$ (close to 25; closest fit overall)

Answer:

$y = 3x - 8$