slope of a line is just like any slope in real life. It's just asking how fast does this slope rise or fall. always remember a slope moves in two directions. In real life the slope of a hill, when looking from the side) moves either up or down and to the right. this is the same as the slope of the line. since the slope moves in 2 directions, it is written as the fraction:
rise/run
this means how fast it goes up or down divided by how fast it moves to the right at the same time.
so given the points (- 2,1) and (1,6), we know that the y values are the up and down movement. The way to look at this is to see which x value comes first. The x values are -2 and 1. so - 2 comes first.
At x = - 2 we see y is 1 and that by the second point it travels upwards to 6. If we want to see how far it rose, we do:
rise = 6 - 1
rise = 5
so now we see how far the line ran in that time and find the difference in x values:
run = 1 -(- 2),
subtracting negative means to add
run = 3
put equation together
rise/run = 5/3
so 5/3 is slope
there is an equation for this but it is always better to explain how the equation was formed if you want to understand future math content.
The equation is
slope = rise/run = (y2 - y1) / (x2 - x1)