Problem Solving

saxenarahul021 wrote:Let ax + by = c, where a,b and c are nonzero constants, be an equation of a line in the standard (x,y) coordinate plane. if (8,12) lies on the line and the x-intercept of the line is 2, what is the value of a/b ?

A. -2
B. -5/4
C. -1
D. -4/5
E. -1/2

Since (8, 12) lies on ax + by = c, so 8a + 12b = c ... Equation 1
Algebraically, an x-intercept is a point on the graph where y is zero, or it is a point in the equation where the y-value is zero.
When y = 0, then ax + 0 = c or ax = c
It is given that x-intercept of the line is 2. So, 2a = c.
Substituting c = 2a in equation 1, we get,
8a + 12b = 2a
6a + 12b = 0
6a = -12b
a/b = -2

The correct answer is A.