What does changing a and b do to the graph of y = a x + b?

What line is the one that is going down as we move from left to right?

y1 = 2 x + 1

y2 = 5/2 x - 2

y3 = Sqrt[12.] x - 4

y4 = -10 x + 2.3

Plot[{y1, y2, y3, y4}, {x, -4, 4}];

Why do all these lines go through the same point?

TableForm[ Table[ a x + 20 , {a, 1, 2, .1}]]

Plot[Evaluate[%], {x, -4, 4}, AspectRatio -> Automatic];

What's different about this next set of lines?
Can you state a general rule?

TableForm[ Table[ -a x + 20 , {a, 1, 2, .1}]]

Plot[Evaluate[%], {x, -4, 4}, AspectRatio -> Automatic];

Describe what is happening in the geometry and the algebra in the following set of lines.

TableForm[ Table[ 2 x + b , {b, 0, 10}]]

Plot[Evaluate[%], {x, -4, 4}, AspectRatio -> Automatic];

Why do all the lines go through the same point?

TableForm[ Table[ a x + a , {a, 1, 2, .1}]]

Plot[Evaluate[%], {x, -4, 4}, AspectRatio -> Automatic];