Question

All of the techniques for finding a line's equation use the definition of slope, which is given the symbol m. slope is defined as the difference between the y coordinates of two points, divided by the difference between the x coordinates of those two points. that is, if you have two points (x1,y1) and (x2,y2) on a line, the slope is m=y2−y1x2−x1. you might be able to remember the definition more easily in the form "the difference in the y values over the difference in the x values." the end result that you want is an equation that looks like y=mx+b, where m is the slope and b is the y intercept—the value of y where the line intersects the y axis. for instance, you might have as the final result the equation y=2x+4. in the example given of distance walked, you could easily determine how far you had walked after 2.5 minutes if you had an equation for the graphed line.

Answer 1

That's a nice story. It's mostly true, but the standard form of a line and the form of a line between two points each avoid a direct expression of the slope.

The standard form for a line is

$ax + by = c$

Either both not both a and b may be zero. When b is zero there's no slope, but it's a perfectly good line.

The line through (a,b) and (c,d) is

$(c-a)(y-b) = (d-b)(x-a)$

Again, we have no slope when a=c but a perfectly good equation and line.