You should know the following:[br]the equation of a horizontal line is in the form [math]y=a[/math];[br]the equation of a vertical line is in the form [math]x=b[/math];[br]In a sloped line [math]l_1[/math], the equation is in the form [math]y=mx+c[/math], where [math]m[/math] is the gradient and [math]c[/math] is the y-intercept.[br][list][*]we can find its gradient given the coordinates of two points on the line.[/*][*]the gradient formula is [math]m=\frac{y_2-y_1}{x_2-x_1}[/math][/*][*]we can find the y-intercept of the [math]l_1[/math] by substituting [math]x=0[/math] and the new-found value of [math]m[/math] into the equation [math]y=mx+c[/math].[br][/*][/list][br]In this activity, you will not only explore the above lines, but also another method to find the equation of a sloped line, given the coordinates of two points on the line.

Consider a general point [math]P(x,y)[/math] lying on the same line in the above applet.[br]Since gradience of AP = gradient of AB, then,[math]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/math].[br]Multiplying both sides, by [math](x-x_1)[/math], we then have[math]y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)[/math][br]Since [math]m=\frac{y_2-y_1}{x_2-x_1}[/math], then the above becomes [math]y-y_1=m\left(x-x_1\right)[/math][br][br]In other words, [b]the general equation[/b] [b]of a sloped line[/b] passing through a point [math]A(x_1,y_1)[/math] is[br][center][b][math]y-y_1=m(x-x_1)[/math][/b][/center]