Question

the x values are 1 through 6 the y values are -1 through -6 it goes from 0 the -6 in a diagonal line what is the rate of this graph

Answer 1

To determine the rate of the graph you described, we can identify the slope of the line formed by the points (1, -1), (2, -2), (3, -3), (4, -4), (5, -5), and (6, -6).

The slope (rate) of a line can be calculated using the formula:

\[
\text{slope} = \frac{\text{change in } y}{\text{change in } x}
\]

From your description, as \( x \) increases from 1 to 6, \( y \) decreases from -1 to -6.

1. For the first pair of values, when \( x = 1 \) and \( y = -1 \), and when \( x = 6 \) and \( y = -6 \):
- Change in \( y \) = \( -6 - (-1) = -6 + 1 = -5 \)
- Change in \( x \) = \( 6 - 1 = 5 \)

Using the slope formula:

\[
\text{slope} = \frac{-5}{5} = -1
\]

So the rate of the graph (slope) is -1. This indicates that for every 1 unit increase in \( x \), \( y \) decreases by 1 unit.