To find the equation of the line given the points [tex]\((10, -2)\)[/tex] and [tex]\((-2, -2)\)[/tex], we follow these steps:
1. Identify the coordinates of the given points:
- [tex]\((x_1, y_1) = (10, -2)\)[/tex]
- [tex]\((x_2, y_2) = (-2, -2)\)[/tex]
2. Calculate the slope [tex]\(m\)[/tex] of the line:
The formula to calculate the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Substitute the given points into the slope formula:
[tex]\[
m = \frac{-2 - (-2)}{-2 - 10} = \frac{0}{-12} = 0
\][/tex]
The slope [tex]\(m\)[/tex] is [tex]\(0\)[/tex].
3. Understand the meaning of the slope:
A slope of [tex]\(0\)[/tex] indicates that the line is a horizontal line. For a horizontal line, the y-coordinate is constant for all x-values.
4. Determine the y-coordinate of the line:
Since the line is horizontal, the y-coordinate of any point on the line is constant. In this case, both given points [tex]\((10, -2)\)[/tex] and [tex]\((-2, -2)\)[/tex] have the y-coordinate of [tex]\(-2\)[/tex].
5. Write the equation of the line:
For a horizontal line where the y-value is constant, the equation of the line is:
[tex]\[
y = \text{constant value}
\][/tex]
Here, the constant y-value is [tex]\(-2\)[/tex]. Thus, the equation of the line is:
[tex]\[
y = -2
\][/tex]
So, the equation of the line is [tex]\(\boxed{y = -2}\)[/tex].
