Question

What is the slope of the line that passes through (4,  3) and (2,  2) ?

Answer 1

For the points you've given, the correct answer is not listed! One way to solve the problem is just to use a graph -- the points are not far away from the origin, and they have whole number coordinates. (See graph.)

Slopt = "rise" / "run"  so to get from (2, 2) to (4, 3), you "rise" +1 and "run" +2. The slope is 1/2.

If the points are (2, 2) and (4, 3), then the slope would be 2.

You can always use a formula to find the slope:

$m=\frac{y_2-y_1}{x_2-x_1}$ which tells the slope of a line joining points $(x_1,y_1)$ and $(x_2,y_2)$.

The formula says

Slope = (second y minus first y) / (second x minus first x)

It always works unless $x_1=x_2$, in which case the line is vertical and has NO defined slope.