mekoner wrote:
My question is:
"Since this is part of the same line", meaning that x = 2y + 5 = y = x/2 -5/2, right? And, should we always re-write the formula in the Y=mx+b form?
a. Yes, that means the line segment is a part of x = 2y+5.
b. Equation of a line can be written in different forms. Once you have enough experience, you can find out the slope without actually using the form. However, writing things out in a recognized form prevents mistakes. At the same time, if you can calculate the slopes mentally or just by observation, you can save computational time. So, to finally answer your question, I would suggest getting familiar with the various forms of equation of a line before doing mental calculations.
Here are a few forms of the top of my head:
1. x/a + y/b = 1 (where a is x intercept and b is y intercept).
2. y = mx + b (where m is the slope and b is the y intercept)
3. (y-y1) = m(x-x1) (where m is the slope and the line passes through (x1,y1)
4. (y-y1) = (x-x1)*(y2-y1)/(x2-x1) (where the line passes through (x1,y1) and (x2,y2)
From comparing the various forms we can see that:
slope = m = -b/a = (y2-y1)/(x2-x1)
and x-intercept = a = -b/m = (x1*y2-x2*y1)/(y2-y1)
Cheers!
