# How to write a general linear equation through two points

We shall have to find a new approach to solving such an equation.

A review of the main results concerning lines and slopes and then examples with detailed solutions are presented. If a line passes through two distinct points P1 x1y1 and P2 x2, y2its slope is given by: This is another interactive tutorial on the slope of a line.

General Equation of a Straight line: The general equation of straight line is given by: For an interactive exploration of this equation Go here. Any straight line in a rectangular system has an equation of the form given above. Slope intercept form of a Line: The equation of a line with a defined slope m can also be written as follows: The above form is called the slope intercept form of a line.

To understand why, go to this interactive tutorial.

Point-Slope form of a line: This is a horizontal line with slope 0 and passes through all points with y coordinate equal to k. This is a vertical line with undefined slope and passes through all points with x coordinate equal to h.

Two non vertical lines are parallel if and only if their slopes are equal.

Find the slope of a line passing through the points 23 and 0-1 -24 and -26 52 and -72 Solution to Example1: The line passing through the given points is a vertical line. Find the slope of a line passing through the points -27 and -2-1 24 and -26 -1-2 and 4Write the general linear equation for the line through the two points (1,1) and (2,3) 1) Do delta(y) over delta(x) to find the slope of the two points.

2) Plug into point-slope equation.

## Slope Intercept Form of the Equation of a line

A linear functionis one that can be written in the form f(x) = mx + b: Here is a more general picture showing two "generic" lines; one with positive slope, and one with negative slope. Now graph the above equation by clicking on two points on the graph as accurately as you can and then pressing.

Bernoulli's equation is nonlinear and cannot be solved by the techniques that we have used to solve first order linear equations. 8 Polking p. 63 Using the substitution $$z = y^{1- n}\text{,}$$ show that we can transform Bernoulli's equation into the linear equation.

Find the equation of a line passing through the point (4, –7) parallel to the line 4x + 6y = 9. 2.