Question

The distance formula between 2 points is given by z=sqrt x^2+y^2 how does this formula relate to the slope of a line

Answer 1

The slope of the can be determined by the formula :

`\text{slope}=(\Delta y)/(\Delta x)`

The quotient of change in y and change in x

While the distance formula which is based on the Pythagorean Theorem,

`d=\sqrt[]{(\Delta x)^2+(\Delta y)^2}`

So basically, the slope is for the calculation on how steep or how much inclination the the line has.

and the distance is merely the calculation of distance or measurement between two points.

Rewriting the formula :

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{distance}=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \end{gathered}`