Question

What is the slope of the line
first point (0, 0) second point (2, -2) third point (4, -4) fourth point (6, -6)

Answer 1

To find the slope of a line determined by two points, you can use the formula for the slope \( m \):

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

Using the first two points \((0, 0)\) and \((2, -2)\):

- \(x_1 = 0\), \(y_1 = 0\)
- \(x_2 = 2\), \(y_2 = -2\)

Plugging in the values:

\[
m = \frac{-2 - 0}{2 - 0} = \frac{-2}{2} = -1
\]

Now, let's check with another pair of points, for example, the second point \((2, -2)\) and the third point \((4, -4)\):

- \(x_1 = 2\), \(y_1 = -2\)
- \(x_2 = 4\), \(y_2 = -4\)

Calculating the slope:

\[
m = \frac{-4 - (-2)}{4 - 2} = \frac{-4 + 2}{2} = \frac{-2}{2} = -1
\]

Finally, checking the slope between the third point \((4, -4)\) and the fourth point \((6, -6)\):

- \(x_1 = 4\), \(y_1 = -4\)
- \(x_2 = 6\), \(y_2 = -6\)

Calculating the slope:

\[
m = \frac{-6 - (-4)}{6 - 4} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1
\]

Thus, the slope of the line connecting the points (0, 0), (2, -2), (4, -4), and (6, -6) is consistently \( -1 \).