Answer: If two distinct points are graphed on a coordinate plane, then the line connecting the points can be represented with a function [tex]f(x)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)+y_1[/tex]. Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two distinct points.
Explanation:
Let the two distinct points on a coordinate plane are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].
The equation of line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Add [tex]y_1[/tex] both sides of the above equation.
[tex]y=\frac{y_2-y_1}{x_2-x_1} (x-x_1)+y_1[/tex]
It is also written as,
[tex]f(x)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)+y_1[/tex]
Where, [tex]x_1, y_1, x_2, y_2[/tex] all are defined real numbers.
