Gradient (also called slope) is the steepness of a line. To determine the gradient, observe the line from left to right: if the line moves up then the gradient is positive, but if the direction is down then the gradient is negative.
The most basic formula for gradient is:
Try the following Geogebra to get a grasp of gradient movements.
Gradient from Linear Equation
The gradient-intercept formula is in the form of:
where m is the gradient and c is the y-intercept.
Equation of a Straight Line
The equation of a straight line is given by:
To find out the equation of a straight line given the gradient and a point, then use the point-intercept formula.
Find the equation of a line that has a gradient of 3 and passes through the point (1, 2).
In the event that two points are given to find the equation of a line, the two-point formula is needed:
Find the equation of a line that passes through the points (2,3) and (4,7).
Parallel and Perpendicular Lines
If two lines are parallel, then they have the same gradient.
Find the equation of a straight line parallel to the line 2x-y-3=0 and passes through (1, -5).
This means that equal gradient lines would not meet because they are on the same direction.
If two lines are perpendicular, then there is a characteristic determined by the gradients of the two lines.
Show that the lines and are perpendicular.