The equation of a line is a mathematical representation of a straight line on a coordinate plane. It is written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.
The slope of a line is determined by the change in y-coordinates over the change in x-coordinates between any two points on the line. This can be calculated using the formula (y2 - y1) / (x2 - x1).
The point-slope form of a line is another way to represent a straight line on a coordinate plane. It is written in the form y - y1 = m(x - x1), where (x1, y1) is a given point on the line and m is the slope of the line.
To find the equation of a line given two points, you can use the slope formula to calculate the slope of the line. Then, you can substitute the slope and one of the given points into the point-slope form of a line to find the equation.
The equation of a plane in 3D space is written in the form Ax + By + Cz + D = 0, where A, B, and C represent the coefficients of the x, y, and z variables respectively, and D is a constant. This equation represents all points that lie on the plane.