Answer to Question #101758 in Algebra for Fernando

Question

One way to find the equation of a line is to look at some points on it and try to find the relationship between the coordinates

Answer 1

Yes. You need only two points.

If A (a_x, a_y) and B (b_x, b_y) are two points on the line then the gradient (slope) of the line is m = (b_y - a_y)/(b_x - a_x) provided b_x ≠ a_x.

From this you can calculate m. Then the general slope-intercept form of the equation is y = mx + c.

Substitute the coordinates of A or B into this equation to find c.

If b_x = a_x then the line is parallel to the y axis and its equation is x = a_x.

There are other methods to find the equation of a straight line.