Find the gradient of the straight line that passes through the points with coordinates (5a,2a) and (5b,2b) .

Question

 Find the gradient of the straight line that passes through the points with coordinates (5a,2a)
and (5b,2b)
.

Answer 1

Gradient is the same as slope between two points.

 

slope = (2b - 2a) / (5b - 5a)

 

 

The 2 and 5 can be factored out.

 

slope = 2(b - a) / 5(b - a)

 

 

(b - a) cancel each out.

 

slope = 2 / 5

 

Gradient is 2/5.

Answer 2

"Gradient" is another word for "slope".

The slope of the line is:

     m  =  (2b-2a)/(5b-5a)
     m  =  (2(b-a))/(5(b-a))
     m = 2/5

To check, insert some numbers:
    Let a=2 and b=3.  points  (10,4) and (15,6)
      m = (6-4)/(15-10)
      m = 2/5

Answer 3

Hi Melanie,

 

Since the gradient is just the slope and the formula is (y2 - y1) / (x2 - x1), the gradient for those coordinates, where (5a, 2a) is (x1, y1):

 

gradient = (2b - 2a) / (5b - 5a)

 

But we can simplify this by taking out the 2 from the top (or numerator) and 5 from the bottom (or denominator):

 

gradient = (2 * (b - a)) / (5 * (b - a))

 

It's a bit hard to see in this horizontal format, but you should notice that (b - a) is on both the top and bottom, so we can cancel that out, since they would divide to equal 1, and we get:

 

gradient = 2 / 5 = 0.4

 

Hope this helps!