Hello, 
What is the slope of THE LINE WHICH CONTAINS THE 
POINTS (-5,2) and (1,4)? 

Plot those two points

 

Draw a green vertical line through the 
point (1,4) and a brown horizontal line through
the point (-5,2) 

 

Now draw a blue line through the points (-5,2) and (1,4)



You now see a right triangle formed by the three 
lines: 

Using the y-axis as a measuring stick, count the number 
of units which is the length of the green vertical side 
of the triangle (the right side of the triangle).  You 
will see that it is 2 units long. This is called the 
RISE.

Now, using the x-axis as a measuring stick, count the 
number of units which is the length of the brown 
horizontal side of the triangle (the bottom side or
base of the triangle.  You will see that it 
is 2 units long.  This is called the RUN.

Now we form the fraction RISE/RUN which is the fraction
2/6 which reduces to 1/3.

Now we observe whether the blue line goes uphill to 
the right or downhill to the right.  When a line goes 
uphill to the right, we give the slope a positive sign, 
and when it goes downhill to the right, we give the 
slope a negative sign.  Since this blue line goes 
uphill to the right, we give its slope a positive sign.

Therefore the slope of the blue line is +1/3

Edwin