Question

What is the slope that passes through 2,5 and -1,5

Answer 1

The slope of the line that passes through the points (2,5) and (-1,5) is 0: it is an horizontal line, because both points have the same y-coordinate. The equation of the line is y=5.

For any two points (x1,y1), (x2,y2), the slope, m, of the line that passes through them can be calculated with:

$m= \dfrac{\Delta y}{\Delta x} = \dfrac{y2-y1}{x2-x1}$

where $\Delta y,\ \Delta x$ represent the increment on the y direction and the increment on the x direction, respectively.

This comes from the definition of "slope": the slope of a line tells you how much does the line grow in the vertical direction for every unit of advance in the x direction.

If you apply the formula to the points given, you get $\Delta y=5-5=0$.