Question

Use the table to answer the question.

x
y

−2
1
2 2
10 4
Determine the slope of the line.

(1 point)
Responses

4
4

−14
negative Start Fraction 1 over 4 End Fraction

−4
negative 4

14

Answer 1

To determine the slope of the line defined by the given points \((-2, 1)\), \((2, 2)\), and \((10, 4)\), we can use the slope formula:

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

We can choose two points to calculate the slope. Let's use the points \((2, 2)\) and \((10, 4)\).

Assigning values:

- \(x_1 = 2, y_1 = 2\)
- \(x_2 = 10, y_2 = 4\)

Now substituting these values into the slope formula:

\[
m = \frac{4 - 2}{10 - 2} = \frac{2}{8} = \frac{1}{4}
\]

Thus, the slope of the line is \(\frac{1}{4}\).

However, it seems that the options provided do not list \(\frac{1}{4}\), but it was mentioned as "negative Start Fraction 1 over 4 End Fraction". Since it doesn't make sense in this context, I'll check the other points and see if they give us the same slope.

Calculating the slope using the first two points \((-2, 1)\) and \((2, 2)\):

Assigning values:

- \(x_1 = -2, y_1 = 1\)
- \(x_2 = 2, y_2 = 2\)

Now substituting these values into the slope formula:

\[
m = \frac{2 - 1}{2 - (-2)} = \frac{1}{4}
\]

Next, checking between the second and third points, \((2, 2)\) and \((10, 4)\):

- \(x_1 = 2, y_1 = 2\)
- \(x_2 = 10, y_2 = 4\)

Yielding the same result:

\[
m = \frac{4 - 2}{10 - 2} = \frac{2}{8} = \frac{1}{4}
\]

Since the slope calculated using both methods remains constant at \(\frac{1}{4}\), which does not align neatly with the options given. Reviewing the provided answers:

- 4
- −14
- −4
- 14

It appears there may be a misunderstanding or mislabeling. The accurate and confirmed slope is indeed \(\frac{1}{4}\). Please double-check the options for an accurate response. The correct answer appears consistently to be \(\frac{1}{4}\).