Write+equations+of+lines+when+given+two+points+and+write+equations+of+lines+from+a+graph

Emma Wheatley, Emmi Shearman, Katherine King, Makenzie Carter
Necessary Formulas:

1. Y=mx+b 2. (y-y1)=m(x-x1) 3. __y2-y1__ x2-x1 4. __rise__ run





by Emma Wheatley

Emmi Shearman

The line through two distinct points (x 1, y 1 ) and (x 2 , y 2 ) is given by


 * (1) || y = y1 + [(y2 - y1) / (x2 - x1)]·(x - x1), ||

where x1 and x2 are assumed to be different. In case they are equal, the equation is simplified to


 * || x = x1 ||

and does not require a second point. Equation (1) can also be written as


 * || y - y1 = [(y2 - y1) / (x2 - x1)]·(x - x1), ||

or even as


 * || (x2 - x1)·(y - y1) = (y2 - y1)·(x - x1), ||

where one does not have to worry whether x1 = x2 or not. However, the simplest for me to remember is this


 * || (y - y1)/(y2 - y1) = (x - x1)/(x2 - x1) ||

which is not as universal is the one before.

Practice Problems and Helpful websites. Katherine King

Things to know
 * equation of line: y=mx+b
 * m is the slope
 * b is the y-intercept
 * The slope of a line - a measure of how fast the line "goes up" or "goes down".
 * A large slope means the line goes up or down really fast (a very steep line).
 * Small slopes means the line isn't very steep.
 * A slope of zero means the line has no steepness at all; it is perfectly horizontal.
 * Equation for the slope

Write the equation of the line when given the points (3,2) (7,4) Answer : y = 1/2x+1/2

Websites Help website 1 Help Website 2

Makenzie Carter Formulas: Slope: for a given two points, (x1, y1) and (x2, y2); m = __y2 - y1__ x2 - x1 Slope- Intercept Equation: y = mx + b

Point- Slope Equation: for a given point (x1, y1) and slope, m, (y - y1) = m(x - x1)

Example: Find the slope of the line Work: m = __y2 - y1__ x2 - x1

m = __3 - (-3)__ -3 - 1

m = __6__ -4

m = - __3__ 2