Question

Use the table to answer the question.

x y
−1 6
1 9
3 12
Use the data from the table to determine the slope of the line.

(1 point)
Responses

3
3

32
Start Fraction 3 over 2 End Fraction

23
Start Fraction 2 over 3 End Fraction

30

Answer 1

To determine the slope of the line defined by the points in the table, we can use the formula for the slope \( m \):

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use the points \((-1, 6)\) and \( (1, 9) \):

- \( x_1 = -1 \), \( y_1 = 6 \)
- \( x_2 = 1 \), \( y_2 = 9 \)

Now we can plug these values into the slope formula:

\[
m = \frac{9 - 6}{1 - (-1)} = \frac{3}{1 + 1} = \frac{3}{2}
\]

Now, let's double-check using another pair of points, \((1, 9)\) and \((3, 12)\):

- \( x_1 = 1 \), \( y_1 = 9 \)
- \( x_2 = 3 \), \( y_2 = 12 \)

Using the slope formula again:

\[
m = \frac{12 - 9}{3 - 1} = \frac{3}{2}
\]

Thus, the slope of the line is \( \frac{3}{2} \).

So, the correct answer is:

**Start Fraction 3 over 2 End Fraction (3/2)**.