Question

the table below shows the number of grams of carbohydrates, x, and the number of calories, y, of six different foods.

carbohydrates (x)	calories (y)
9.5	138
10	147
6	89
7	108
4	62

which of the following is the linear equation that best matches the data?

○ ( y = 15x )

○ ( y = 0.07x )

○ ( y = 0.1x - 0.4 )

○ ( y = 14.1x + 5.8 )

Explanation:

Step1: Test the first option \( y = 15x \)

For \( x = 8 \), \( y = 15\times8 = 120 \) (matches). For \( x = 9.5 \), \( y = 15\times9.5 = 142.5 \), but the actual \( y \) is 138 (close but not exact). For \( x = 10 \), \( y = 15\times10 = 150 \), actual \( y = 147 \) (close). For \( x = 6 \), \( y = 15\times6 = 90 \), actual \( y = 89 \) (very close). For \( x = 7 \), \( y = 15\times7 = 105 \), actual \( y = 108 \) (close). For \( x = 4 \), \( y = 15\times4 = 60 \), actual \( y = 62 \) (close).

Step2: Test the second option \( y = 0.07x \)

For \( x = 8 \), \( y = 0.07\times8 = 0.56 \), which is way off from 120. So this is incorrect.

Step3: Test the third option \( y = 0.1x - 0.4 \)

For \( x = 8 \), \( y = 0.1\times8 - 0.4 = 0.4 \), way off from 120. Incorrect.

Step4: Test the fourth option \( y = 14.1x + 5.8 \)

For \( x = 8 \), \( y = 14.1\times8 + 5.8 = 112.8 + 5.8 = 118.6 \), not 120. For \( x = 9.5 \), \( y = 14.1\times9.5 + 5.8 = 133.95 + 5.8 = 139.75 \), not 138. Less accurate than the first option.

Comparing all, \( y = 15x \) gives the closest values to the actual data points overall.

Answer:

\( y = 15x \)