New way of finding out equation of a line

[gmatrant]

I have come across a point slope formula to calculate the equation of the line.
y-y1 = m(x-x1).
But i don't understand this approach

The explanation is from Kaplan's website
But in the explanation below I don't understand how he calculates the slope of the line. Why does he move 6 units to the right from the point marked (-6,-1). Can someone explain what is the approach here.

[mschling52]

He is trying to find the y-intercept of the line, which is the y-coordinate of the point where the line intersects the y-axis (in other words, the y-coordinate of the point where x=0). He moves six units to the right from the point (-6,-1) because moving 6 units to the right in the horizontal direction will get you to the point where x=0.

[moneyman]

When 6 points are moved to the right the line climbs by 11 1/4 then shouldnt the y intercept be 11 1/4?? Why is it 10 1/4??

[gmatrant]

When 6 points are moved to the right the line climbs by 11 1/4 then shouldnt the y intercept be 11 1/4?? Why is it 10 1/4??

11 1/4 up, so (6,-1) when moved along the slope i.e 11 1/4 is
11 1/4 + (-1) = 10 1/4.

Did you get it?

[moneyman]

Oh yeah!! It completely makes sense now. I cant believe I dint notice that. Thanks