Question

The graph of a linear function z is shown below.
A two-dimensional graph, with a horizontal x-axis and a vertical y-axis, displays a straight line. The line slopes downward from left to right. Two points are marked on the line: (-2, 6) and (5, -4.5). The graph is a coordinate plane, and the axes are labeled with numbers for the x and y values. The graph has a grid to aid in accurate plotting of points.
Which of the following best describes the slope of function z?
Responses

A. -2/3
B. 3/2
C. -3/2
D. 2/3

Answer 1

To find the slope of the linear function represented by the points (-2, 6) and (5, -4.5), we can use the formula for the slope \( m \) given two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Substituting the given points:

- \((x_1, y_1) = (-2, 6)\)
- \((x_2, y_2) = (5, -4.5)\)

Now substituting values into the slope formula:

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

Calculating the numerator:

\[
-4.5 - 6 = -10.5
\]

Now calculating the denominator:

\[
5 - (-2) = 5 + 2 = 7
\]

Now putting it all together:

\[
m = \frac{-10.5}{7}
\]

We can simplify this fraction:

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

Thus, the slope of function z is:

**C. -3/2**