Question

If two distinct points are graphed on a coordinate plane, then the line connecting the points can be represented with a function.

Answer 1

Answer: If two distinct points are graphed on a coordinate plane, then the line connecting the points can be represented with a function $f(x)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)+y_1$. Where $(x_1,y_1)$ and $(x_2,y_2)$ are two distinct points.

Explanation:

Let the two distinct points on a coordinate plane are $(x_1,y_1)$ and $(x_2,y_2)$.

The equation of line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is defined as

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

Add $y_1$ both sides of the above equation.

$y=\frac{y_2-y_1}{x_2-x_1} (x-x_1)+y_1$

It is also written as,

$f(x)=\frac{y_2-y_1}{x_2-x_1} (x-x_1)+y_1$

Where, $x_1, y_1, x_2, y_2$ all are defined real numbers.