GRADIENT 1

A line passes through (2a, 7) and (8, 5a). If its slope is 2, find a.

Solution

x1=2a, y1 = 7, x2 = 8, y2 = 5a

Slope(m) =    y2 – y1

                     x2 – x1

               2 =  5a – 7

                      8 – 2a

    2 =    5a – 7     [cross multiplying]

   1       8 – 2a

2(8 – 2a) = 5a – 7

16 – 4a = 5a – 7

16 – 8a + 7 = 5a

16 + 7 = 5a+ 8a

23 = 13a

23 = 13a

13    13

23/13 = a

Hence a = 23/13

TRY THIS.................................

A line passes through (2a, 7) and (1, 4a). If its slope is 8, find a.