3: Slope of a line - gradient rise over run of a line. Coordinate geometry of the line maths course
Learn how to find the slope of a line using the slope formula y2-y1/x2-x1 or the gradient of the line using rise over run.
If given the coordinates of two points on the line, they can be substituted into the slope formula from coordinate geometry.
If given a graph with the line plotted then the formula for slope or gradient of rise over run can be used. We start by constructing a right angled triangle with the line as the hypotenuse. The vertical side is the rise and the horizontal side is the run. The lengths of the rise and run can be read directly from the axis.
The slope can also be found if given the angle made with the positive sense of the x-axis. The tan θ theta of the angle is the slope of the line.
The slopes of parallel and perpendicular lines can also be found as parallel lines have equal slopes and perpendicular lines have slopes that are negative reciprocals of each other.
Finding the slope of a line from its equation requires the use of the formula -a over b. -a/b If the angle made by the line with the positive sense of the x-axis is known then tan theta of the angle will yield the slope.
This module covers the Leaving Certificate ordinary level LCOL maths course. If you require higher level maths LCHL then check out my course on Coordinate geometry of the line on Udemy.
Coordinate geometry is also known as Cartesian Maths and Analytical Geometry.
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