(4,2) and (9,5)

Question

Find the slope between each pair of point

 

Answer 1

Casey, 

 

This is just an application of the standard method of finding the slope of a line between to points.  Sometimes its helpful to plot the two points on graph paper or sketch and draw a line connecting them.

 

Point 1 is (x1, y1) = (4, 2) and point 2 is (x2, y2) = (9, 5)

 

The slope is the difference between the two y values (y2-y1) divided by the difference between the two x values (x2-x1).  This is sometimes stated as the slope = rise/run, which is height along y (the rise) divided by length along x (the run).

 

slope = (y2-y1)/(x2-x1) = (5-2)/(9-4) = 3/5.  

Answer 2

To find the line connecting these two points, first consider the general form of a line;

 

Y=Mx+B

 

Since you want these two points to be on this line, we know the following relations must be satisfied:

 

2=4M+B

5=9M+B

 

This is a system of two equations, with two unknowns. From here we must use algebra! From the first equation we know

 

B=2-4M

 

and if we insert this into the second equation, we'll find

 

5=9M+2-4M

 

Solving this for M;

 

5M=3

M=3/5

 

I suppose this is where your real question would end, and we could say the slope is 3/5 (three fifths).

 

However we could of also found the slope using the simple "rise over run" method:

 

Change in Y=5-2=3

Change in X=9-4=5

 

M=Change in Y/Change in X=3/5

 

And if you need the full equation, simply solve for B!

 

B=2-4M

B=2-4(3/5)

B=2-12/5

B=(10-12)/5

B=-2/5

 

Thus Y=(3/5)x-(2/5)

 

Hope this helps!