Question

each day, talisa exercises by first stretching and then swimming some laps, as shown in the table. use the table of her exercise data.
which could be an equation of a trend line for the data?
a ( y=\frac{1}{2}x + 15 )
b ( y = 2x+15 )
c ( y=\frac{1}{2}x + 25 )
d ( y = 2x+25 )

Explanation:

Step1: Substitute \(x = 5\) into each equation

• For \(y=\frac{1}{2}x + 15\): \(y=\frac{1}{2}\times5+15=\frac{5}{2}+15 = 2.5 + 15=17.5

eq25\)

• For \(y = 2x+15\): \(y=2\times5 + 15=10 + 15=25\)
• For \(y=\frac{1}{2}x+25\): \(y=\frac{1}{2}\times5+25=\frac{5}{2}+25=2.5 + 25 = 27.5

eq25\)

• For \(y=2x + 25\): \(y=2\times5+25=10 + 25=35

eq25\)

Step2: Substitute \(x = 6\) into the remaining possible equation (\(y = 2x+15\))

\(y=2\times6+15=12 + 15=27\approx28\)

Step3: Substitute \(x = 7\) into \(y = 2x+15\)

\(y=2\times7+15=14 + 15=29\)

Step4: Substitute \(x = 8\) into \(y = 2x+15\)

\(y=2\times8+15=16 + 15=31\approx30\)

Step5: Substitute \(x = 9\) into \(y = 2x+15\)

\(y=2\times9+15=18 + 15=33\approx32\)

Answer:

B. \(y = 2x+15\)