Writing Linear Equations
Video: Write the equation for a line from two points. (Patrick JMT)
More on Point Slope Form of a Linear Equation (AoPS)
Hopefully, we remember how to write linear equations in slope-intercept (y=mx+b) form, where m is the slope, and b is the y-intercept.
EXAMPLE: Write an equation for a line with a slope of 6 and a y-intercept of -5. ANSWER: y = 6x – 5.
We might not remember how to write other forms of equations for lines, even though some of these are much easier to use in more situations. The big dog of linear equations is point-slope form of a linear equation.
We can use this form of a linear equation to write an equation quickly knowing the slope and ANY point on the line. Check it out:
EXAMPLE: slope = 1/3, point = (-1,8)
Point-slope looks like this: 
, where m is the slope, and (x1, y1)
is the point we know.
ANSWER: y – 8 = 1/3(x + 1). Done. No rearranging necessary.
Parallel and Perpendicular lines.
Two lines that are parallel, have the same slope.
Two lines that are perpendicular, have slopes that multiply to -1. In other words, negative reciprocal slopes.
EXAMPLE: The slope of a line perpendicular to y = -3/2 x +1 is 2/3. We took the reciprocal of -3/2, and made it positive. BAM!