Describe the process for finding the equation of a line if you are given two points on the line?

Answer 1

Let the 2 points be (x1,y1) and (x2,y2)

eqn of line s given by

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

where (y2-y1)/(x2-x1) is the slope of line

Answer 2

You are given (x1, y1) and (x2, y2) as points on a line.

The first step is to find the slope.
m = (y2 - y1) / (x2 - x2), where m is the slope.
*You could think of this equation as the difference between the y values (rise) divided by the difference between the x values (run).

Once you know the slope, substitiute the slope's value and the coordinates of either point into the point-slope equation.
y - y1 = m(x - x1); where m is the slope and (x1, y1) is a known point on the line.

Simplify this into the form needed, ususally either slope-intercept form (y = mx + b) or standard form (Ax + Bx = C; where a, b, and c are real numbers).

Example:Find the equation to the line that has the points (-4, -1) and (3, 4).
m = (y2 - y1) / (x2 - x1)
m = (4 - (-1)) / (3 - (-4))
m = 5 / 7

y - y1 = m(x - x1)
y - (-1) = (5/7)(x - (-4))
y + 1 = (5/7)x + (20/7) --- Subtract 1 from each side...
y = (5/7)x + (13/7) --- This is slope-intercept form. To transfer this to standard form, subtract (5/7)x from both sides...
-(5/7)x + y = (13/7) --- Multiply every thing by 7...
-5x + 7y = 13 --- This is standard form.

Answer 3

The really easy way is to graph it and then find the slope and the intercept, but you can compute