Linear equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables.

A common form of a linear equation in the two variables x and y is

where m and b designate constants. The origin of the name linear comes from the fact that the set of solutions of such an equation forms a straight line in the plane. In this particular equation, the constant m determines the slope or gradient of that line, and the constant term b determines the point at which the line crosses the y-axis, otherwise known as the y-intercept.

General form of a linear equation

where A and B are not both equal to zero. The equation is usually written so that A ≥ 0, by convention. The graph of the equation is a straight line, and every straight line can be represented by an equation in the above form. If A is nonzero, then the x-intercept, that is the x-coordinate of the point where the graph crosses the x-axis (y is zero), is -C/A. If B is nonzero, then the y-intercept, that is the y-coordinate of the point where the graph crosses the y-axis (x is zero), is -C/B, and the slope of the line is -A/B.

Point slope form

The equation of a line having the slope and one point is given by:

where m is the slope of the line and (x1,y1) is any point on the line. The point-slope and slope-intercept forms are easily interchangeable.

The point-slope form expresses the fact that the difference in the y coordinate between two points on a line (that is, y - y1) is proportional to the difference in the x coordinate (that is, x - x1). The proportionality constant is m (the slope of the line).

Point slope refers to a method for graphing a linear equation on an x-y axis. When graphing a linear equation, the whole idea is to take pairs of x's and y's and plot them on the graph. While you could plot several points by just plugging in values of x, the point-slope form makes the whole process simpler. Point-slope form is also used to take a graph and find the equation of that particular line.

Point slope form gets its name because it uses a single point on the graph and the slope of the line.

Point-slope form is all about having a single point and a direction (slope) and converting that between an algebraic equation and a graph.As you can see, point-slope form is nothing too complicated. It is just one way of writing an equation for a line.