The equation of a line is an equation which connects the x and the y values for every point on the line. When graphed, all the pairs ([i]x[/i],[i]y[/i]) that are a solution of this equation form the line.[br][br]Using the gradient formula, the position of a general point ([i]x[/i],[i]y[/i]) on a line with gradient m passing through [math]\left(x_A,y_A\right)[/math] , is given by [math]\frac{y-y_A}{x-x_A}=m[/math]. [br]Rearranging, we find[b] the equation of the line[/b] is [math]y-y_A=m\left(x-x_A\right)[/math][br][br]If we further rearrange this equation, we can get the [b]gradient-intercept form[/b] of the equation of the line: [math]y=mx+c[/math][br][br]In [b]general form[/b], the equation of a line is [math]ax+by=d[/math] where [i]a[/i], [i]b[/i], [i]d[/i] are constants.[br]

A horizontal line has gradient [math]m=0[/math]. This means the equation of a horizontal line is [math]y=y_A[/math] (if we know that it goes through point [math]A\left(x_A,y_A\right)[/math]) or in general [math]y=c[/math].[br][br]A vertical line has an equation [math]x=x_A[/math] (if we know that it goes through point [math]A\left(x_A,y_A\right)[/math]) or in general [math]x=k[/math]. These lines do not have a gradient.

In the next applet, you can move A and B to modify the line and observe the changes in the equations. You can switch from the Point-Gradient form and the Gradient-Intercept form using the checkboxes.