a_1/a_2

b_1/b_2

c_1/c_2

Line2

If a1/a2=b1/b2, then the two lines have the same slope, are parallel.
(the two linear equations do not have a solution)
If a1/a2=b1/b2=c1/c2, then the two lines are co-incident
(the two equations have infinite solutions)
in all other cases, the two lines intersect
(the two equations have a single solution)

Pair of linear equations

In case of a pair of linear equations 
(two lines in the same plane), 
what are the solution possibilities?

Slope

a_1 = 2 (slider from -10 to 10, step 1)
b_1 = 2 (slider from -10 to 10, step 1)
c_1 = 4 (slider from -20 to 20, step 1)
Line1: (a_1 * x) + (b_1 * y) + c_1 = 0
A = Point(Line1)
a_2 = 4 (slider from -5 to 10, step 1)
b_2 = 4 (slider from -10 to 10, step 1)
c_2 = -6 (slider from -10 to 10, step 1)
a = false
text2: "" + b_1 + "/" + b_2 + "=" + (b_1 / b_2) + ""
b = false
text3: "" + c_1 + "/" + c_2 + "=" + (c_1 / c_2) + ""
c = false
Line2: (a_2 * x) + (b_2 * y) + c_2 = 0
d = false
C = Point(Line2)
D = Intersect(Line1, yAxis)
text4: "Equation of the line is ax+by+c=0, which is " + a_1 + "x+" + b_1 + "y + " + c_1 + " = 0

Slope of the line is -a/b, which is  -(" + a_1 + "/ " + b_1 + ") 

Y axis intercept is -c/b, which is -(" + c_1 + "/" + b_1 + ")"
F = Intersect(Line1, Line2)
text1: "" + a_1 + "/" + a_2 + "=" + (a_1 / a_2) + ""
g = false
E = Intersect(Line1, xAxis)
text7: "slope of Line1 =-" + a_1 + "/" + b_1 + "
slope of Line2 = -" + a_2 + "/" + b_2 + ""
e = false

Tool: SquareTool
Tool2[ <Number>, <Point> ]
Input: side, A
Output: poly1

B = Point(Circle[A, side])
a = Segment(A, B)
c = Circle(A, side)
b = OrthogonalLine(A, a)
C = Intersect(c, b, 2)
d = Circle(C, side)
e = OrthogonalLine(C, b)
D = Intersect(d, e, 1)
poly1, a_1, b_1, d_1, c_1 = Polygon(A, B, D, C)