Question

graph the line $y = -6$ on the axes shown below.
type of line: choose one
y
10
9
8
7
6
5
4
3
2
1
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 x
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10

Explanation:

Step1: Analyze the equation \( y = -6 \)

The equation \( y = -6 \) represents a horizontal line because for any value of \( x \), the value of \( y \) remains constant at -6. In the slope - intercept form \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept), for \( y=-6 \), we can rewrite it as \( y = 0x-6 \). The slope \( m = 0 \), which is the characteristic of a horizontal line.

Step2: Determine the type of line

Since the slope of the line \( y=-6 \) is 0, the line is horizontal. To graph it, we find the point on the y - axis where \( y=-6 \) (the y - intercept is \( (0,-6) \)) and then draw a straight horizontal line passing through this point (and all other points with \( y=-6 \) regardless of the value of \( x \)).

Answer:

Type of line: Horizontal
To graph the line: Plot the point \( (0, - 6) \) on the coordinate plane. Then, draw a straight horizontal line passing through this point, extending infinitely in both the positive and negative \( x \) - directions (since for every \( x \) - value, \( y=-6 \)).