Question

X is partly constant and partly varies with y.when y=5,x=19 and when y =10,x=34. A. Find the relationship between x and y . B. hence find x when y =7

Answer 1

slope = m = (Y2 - Y1)/ (X2 - X1) = (10 - 5) / (34 - 19) = 5/15 = 1/3
so if y = m x + b
y = (1/3) x + b
now put a point in
5 = (1/3)19 + b
15 = 19 + 3 b
3 b = -4
b = -4/3
so
y = (1/3) x - 4/3
or
3 y = x - 4
if y = 7
21 =x - 4
x = 25

Answer 2

or, by the wording of the question:
"X is partly constant and partly varies with y"
means
x = ky + b
using y=5,x=19 ---> <b>19 = 5k + b</b>
using y =10,x=34 --> <b>34 = 10k + b</b>
subtract them: 5k = 15, k = 3, then from 19 = 5k + b, b = 4
<b>x = 3y+4</b>
so when y = 7
x = 3(7) + 4 = 25