Question

Write equations for three lines that intersect to form a triangle

Answer 1

1.
Any 3 lines a, b and c intersect and form triangles, in no 2 of them are parallel.


2.

2 lines are parallel only if their slopes are equal.


3.

if the equation of a line l is given in the form y=mx+t, then m, the coefficient of x, is the slope of that line.


4.

so given lines a, b, c with equations:


`a: y=m_1x+t\\\\b: y=m_2x+u\\\\c: y=m_3x+v`

if
`m_1 \\eq m_2 \\eq m_3`, then the lines intersect, forming thus a triangle.


5.

let the 3 lines be:


`a: y=2x+5\\\\b: y=-4x+13\\\\c: y=x+7`