The Equation of a Straight Line (y = mx + c)

The Gradient: Understanding and Implementing

The gradient of a line is effectively its ‘steepness’.
The gradient (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
The idea of gradient can be pictorially represented as ‘rise over run’.
The negative gradient signifies that the line slopes downwards as it moves from the left to right.
A line that goes straight across (horizontal) has a gradient of zero.

Lines that are parallel share the same gradient.
Lines that are perpendicular have slopes that multiply together to give -1. So if Line 1 has gradient m1 and Line 2 has gradient m2, for the lines to be perpendicular, m1 * m2 = -1.

The distance between two points can be calculated using Pythagoras’ theorem: √[(x_2-x_1)² + (y_2-y_1)²].
This forms the hypotenuse of a right triangle, where the horizontal and vertical distances between the two points are the other two sides of the triangle.

Any point lying between two given points (x1, y1) and (x2, y2) on a line can be found by using a ratio formula: (x, y) = ((1-k)x1+ kx2 , (1-k)y1+ ky2).
By adjusting the value of k (which is the ratio), we can adjust where the point is on the line.

The equation of a straight line can be written in the form y = mx + c, where m is the gradient and c is the y-intercept.
The y-intercept is the point where the line intersects (crosses) the y-axis.
The gradient can be found from the slope-intercept form of the equation by looking at the coefficient in front of the x variable.