Question

What is the slope of the linear relationship shown on the graph?

a graph of a line that passes through the points 0 comma negative 2 and negative 2 comma 1

negative two thirds
two thirds
negative three halves
three halves

Answer 1

To determine the slope of the linear relationship shown on the graph, we can use the formula for the slope \( m \) given two points \((x_1, y_1)\) and \((x_2, y_2)\):

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

Let's use the points \( (0, -2) \) and \( (-2, 1) \):
- \( (x_1, y_1) = (0, -2) \)
- \( (x_2, y_2) = (-2, 1) \)

Now, substitute these values into the slope formula:

\[
m = \frac{1 - (-2)}{-2 - 0}
\]
\[
m = \frac{1 + 2}{-2}
\]
\[
m = \frac{3}{-2} = -\frac{3}{2}
\]

So the slope of the linear relationship is \( -\frac{3}{2} \).

The correct answer is **negative three halves**.