The Slope of A Line
|Identify a few concepts on |
(i) gradient properties
(ii) equation of a line
(iii) trigonometry and gradient and
(iv) collinearity from the article below.
Post as comment.
When the slope of the line is 0, you know that the line is horizontal and you know it's a vertical line when the slope of a line is undefined.
In the Figures below, the subscripts on point A, B and C indicate the fact that there are three points on the line. The change in y whether up or down is divided by the change in x going to the right, this is the 'rise over run' concept.
y = mx + b is the equation that represents the line and the slope of the line with respect to the x-axis which is given by tan q = m. This is the slope-intercept form of the equation of a line. (m for slope? Seems to be the standard!)
When the slope passes through a point A(x1, y1) then y1 = mx1 + b or with subtraction
y - y1 = m (x - x1)
You now have the slope-point form of the equation of a line.
You can also express the slope of a line with the coordinates of points on the line. For instance, in the above figure, A(x, y) and B(s, y) are on the line y= mx + b :
m = tan q = therefore, you can use the following for the equation of the line AB:
The equations of lines with slope 2 through the points would be:
For (-2,1) the equation would be: 2x - y + 5 = 0.
For (-1, -1) the equation would be: 2x - y + 1 = 0