4: Equation of a line - algebraic ax+by+c=0 or y=mx+c Coordinate geometry of the line maths course
Learn how to find the equation of a line using the formula y-y1=m(x-x1) or y=mx+c
If given the coordinates of two points on the line, the slope can be found using the slope formula which can then be substituted for m in the formula with one point to find the equation.
If given a graph with the line plotted then the formula for slope 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. We can then find the y intercept. Using the equation of a line formula y=mx+c we can substitute the slope for m and the y intercept for c in order to find the equation of the line.
The equations of parallel and perpendicular lines are very similar. Parallel lines have the same coefficients for the x and y terms but different constant terms. Perpendicular lines have their x and y term coefficients swapped. The new y term coefficient has a change in sign also. The constant terms will be different.
This module covers the Leaving Certificate ordinary level maths LCOL 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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