Question

Which is the equation of a trend line that passes through the points (3, 95) and (11, 12)? Round values to the nearest ten-thousandths.
y = negative 10.375 x + 126.125
y = negative 0.096 x + 13.056
y = 0.096 x + 10.944
y = 10.375 x 63.875

Answer 1

To find the equation of the trend line (in the form \( y = mx + b \)) that passes through the points (3, 95) and (11, 12), we need to determine the slope \( m \) and the y-intercept \( b \).

### Step 1: Calculate the slope \( m \)

The slope formula is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (3, 95) and (11, 12):
- \( (x_1, y_1) = (3, 95) \)
- \( (x_2, y_2) = (11, 12) \)

Substituting the values in:
\[
m = \frac{12 - 95}{11 - 3} = \frac{-83}{8} = -10.375
\]

### Step 2: Find the y-intercept \( b \)

Using the slope-intercept form \( y = mx + b \), we can substitute in one of the points to solve for \( b \). We'll use the point (3, 95):

\[
95 = -10.375(3) + b
\]
\[
95 = -31.125 + b
\]
\[
b = 95 + 31.125 = 126.125
\]

### Step 3: Write the equation of the trend line

The final equation of the trend line is:
\[
y = -10.375x + 126.125
\]

Now we round the values if necessary (though they are already in the desired form).

### Conclusion

The equation of the trend line is:
\[
\text{y = -10.375 x + 126.125}
\]

Thus, the correct option is:
\[
\text{y = negative 10.375 x + 126.125}
\]