Question

Two points defining a linear function are shown in the table below.

x
y
–14
–18
–10
–12

What is the slope of the function?
Two-thirds
Three-halves
2
6

Answer 1

To find the slope of the linear function defined by the two points in the table, we first need to identify the points. The points given are:

- Point 1: \((-14, -18)\)
- Point 2: \((-10, -12)\)

The slope \(m\) of a linear function is calculated using the formula:

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

Let’s assign values to \(x_1, y_1, x_2, y_2\):

- \(x_1 = -14\)
- \(y_1 = -18\)
- \(x_2 = -10\)
- \(y_2 = -12\)

Now we can plug these values into the slope formula:

\[
m = \frac{-12 - (-18)}{-10 - (-14)}
\]

This simplifies to:

\[
m = \frac{-12 + 18}{-10 + 14}
\]
\[
m = \frac{6}{4}
\]
\[
m = \frac{3}{2}
\]

Thus, the slope of the function is **Three-halves**.