Sure, let's break down the problem step by step.
### Part 1: Determine the Slope of the Line
To determine the slope of a line that passes through two points, we use the slope formula:
[tex]\[
\text{slope} \, (m) = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the two points.
In this problem, we have the points (5, 2) and (-1, 2). Let's label them:
- [tex]\(x_1 = 5\)[/tex]
- [tex]\(y_1 = 2\)[/tex]
- [tex]\(x_2 = -1\)[/tex]
- [tex]\(y_2 = 2\)[/tex]
Now, substitute these values into the slope formula:
[tex]\[
m = \frac{2 - 2}{-1 - 5}
\][/tex]
Simplify the numerator and the denominator:
[tex]\[
m = \frac{0}{-6}
\][/tex]
Since the numerator is 0, the entire fraction evaluates to 0:
[tex]\[
m = 0
\][/tex]
So, the slope of the line that contains the points (5, 2) and (-1, 2) is 0.
### Part 2: Determine the Type of Line
To determine the type of line, we look at the value of the slope:
- If the slope is 0, the line is horizontal.
- If the slope is undefined (division by zero), the line is vertical.
- If the slope is a positive or negative number (other than zero), the line is diagonal, either rising or falling.
In this case, the slope is 0. This means that the line is horizontal.
To support this, remember that a horizontal line means that the y-coordinate is constant for any value of the x-coordinate. In our points (5, 2) and (-1, 2), you can see that the y-coordinate is the same (both are 2) indicating that the line does not rise or fall as x changes — it remains flat.
So, the line that passes through the points (5, 2) and (-1, 2) is a horizontal line.
