Question

The graph of a linear function z is shown below. (-2, 6) and (5, -4.5)
Which of the following BEST describes the slope of function z?

-2/3
3/2
-3/2
2/3

Answer 1

To find the slope of the linear function \( z \) represented by the points (-2, 6) and (5, -4.5), we can use the slope formula:

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

where \((x_1, y_1)\) is the first point \((-2, 6)\) and \((x_2, y_2)\) is the second point \((5, -4.5)\).

Substituting in the values:

\[
x_1 = -2, \quad y_1 = 6, \quad x_2 = 5, \quad y_2 = -4.5
\]

Now, plug these into the slope formula:

\[
m = \frac{-4.5 - 6}{5 - (-2)} = \frac{-4.5 - 6}{5 + 2} = \frac{-10.5}{7}
\]

Now, simplify \(-10.5\) over \(7\):

\[
m = -\frac{10.5}{7} = -\frac{21}{14} = -\frac{3}{2}
\]

Thus, the slope of the function \( z \) is \(-\frac{3}{2}\).

Hence, the BEST description of the slope of function \( z \) is:

\(\boxed{-\frac{3}{2}}\)