Write an equation for three lines that intersect to form a triangle

Answer 1

Questions like this make it easy to give simple, even obvious, answers:

y = 0 [that is, the x-axis]

x = 0 [that is, the y-axis]

y = -x + 1 [that is the line containing (0,1) and (1,0), the down-sloping line that completes the triangle]

Answer 2

There are many ways of doing this.....here's one:

Select 3 points for the corners of the triangle.

For each pair of points, write the line equation in the slope-offset format: (y - 1) = m*(x - b)

Example:

3 points:

A: (4, 2)

B: (6, 3)

C: (5, -2)

The lines are AB, AC, and BC. Here is the solution for AB:

1. find the slope: m = (2-3)/(6-4) = -1/2
2. Using the first point for the offsets, write the equation: (y - 2) = -1/2 (x - 4)

Plot everything on graph paper to make sure it all makes sense