Question

Find a and b, if the points P(6,0) and Q(3,2) lie on the graph of ax + by =12

Answer 1

The given equation is:
ax + by = 12
We are given that the two points (6,0) and (3,2) belong to this line. This means that these two points satisfy the equation of the line.
Therefore, to get the value of a and b, we will substitute with the given points in the equation and solve the resulting equations for a and b as follows:

For the point (6,0):
ax + by = 12
a(6) + b(0) = 12
6a = 12
a = 12/6 = 2

For point (3,2):
ax + by = 12
(2)(3) + b(2) = 12
6 + 2b = 12
2b = 12-6 = 6
b = 3

Based on the above calculations:
a = 2 and b = 3, therefore, the equation is:
2x + 3y = 12