Two-Point Problem

This calculator gives information about the line formed by two points on the coordinate plane. If you aren't completely familiar and comfortable with the coordinate plane, click the link above. This help file relies strongly on concepts related to the coordinate plane.

Enter the two coordinates of the endpoints of the line and you will be given the line's slope, distance, equation, y-intercept, and coordinates of its midpoint.

Slope
"Rise over run" is a term I remember well from middle school and high school. A line's slope is the difference between its two values in height divided by the difference between its two horizontal values.

To find the slope of a line, use the equation

Where x1 and y1 are the x and y coordinates of the first point given and x2 and y2 are the x and y coordinates of the second point given. It does not matter which point you use as the "first point" and which you use as the "second point" as long as you keep the coordinates from each separate.

Distance
The distance of a line is the measure of its length; how much space it takes. To find the distance of the line on a coordinate plane use the formula

This formula was derived by making the line the hypotenuse of a right triangle and then using the Pythagorean Theorem to find its value.

Equation (Slope-Intercept Form)
The equation is given in slope-intercept form which is
y = mx + b

Where m is the slope of the line and b is the point at which it crosses the y-axis.

The other forms in which this equation can be given are:
point-slope form
y1 = m(x1 - x2) + y2

or

y1 - y2 = m(x1 - x2)

standard form
ax + by = c

One of my math teachers preferred that we put our equation in slope-intercept form, but he said that standard form was more formal. He would always tell us that if the president of the United States walked in the room we'd have to switch from using slope-intercept form to standard form to impress him.

Y-intercept
The y-intercept of the line is the point in which it crosses the y-axis of the coordinate plane.

This is the point at which the variable b in the slope-intercept form of the line's equation equals zero.

Midpoint
The midpoint of the line is the line's exact center.

This is found with the formula

The first part of this formula will find the x-coordinate of the midpoint and the second part will find its y-coordinate.

Works Cited
Brown, Jeff and Russ Herman. "The Cartesian Plane." UNCW. 1996. UNCW. 18
      July, 2006. <http://www.onlinemathlearning.com/coordinate-geometry.html>.

"Equation of a Line—Point-Slope Form." Zona Land. 1997. Edward A. Zobel. 18 July,
     2006. <http://id.mind.net/~zona/mmts/functionInstitute/linearFunctions/lpsf.html>.