Find the equations of at least three lines that intersect each other at the point (6, -2).

To find the equations of lines that intersect at a specific point, such as (6, -2), we need to consider the slope-intercept form of a linear equation, which is y = mx + b. In this form, m represents the slope of the line, and b represents the y-intercept.

To find the equations of the lines, we need to determine the slopes and y-intercepts of each line that passes through the given point.

Let's start by finding the equation of the first line:
Line 1:

1. Choose an arbitrary slope, say m1 = 2, which represents the slope of the line.
2. Since the line passes through (6, -2), we can substitute these values into the equation:
-2 = 2(6) + b1
Simplifying this, we get: -2 = 12 + b1
By rearranging the equation, we find: b1 = -14

Hence, the equation of the first line is y = 2x - 14.

Now, let's find the equation of the second line:
Line 2:

1. Choose another arbitrary slope, such as m2 = -3.
2. Using the same point of intersection (6, -2), we substitute these values into the equation:
-2 = -3(6) + b2
Simplifying this, we get: -2 = -18 + b2
By rearranging the equation, we find: b2 = 16

So, the equation of the second line is y = -3x + 16.

Finally, let's find the equation of the third line:
Line 3:

1. Choose a different slope, for example, m3 = 1/2.
2. Substitute the values of the point (6, -2) into the equation:
-2 = (1/2)(6) + b3
Simplifying this, we get: -2 = 3 + b3
By rearranging the equation, we find: b3 = -5

Therefore, the equation of the third line is y = (1/2)x - 5.

To summarize, the equations of at least three lines that intersect at the point (6, -2) are:
- Line 1: y = 2x - 14
- Line 2: y = -3x + 16
- Line 3: y = (1/2)x - 5

Just use the point-slope form and pick any three values for the slope m:

y+2 = m(x-6)