sandy wrote:
In the xy-coordinate plane, lines j and k intersect at point (1, 3). If the equation of line j is y = ax + 10, and the equation of k is y = bx + a, where a and b are constants, what is the value of b?
We're told that the point (1, 3) lies on line j
So, it must be the case that x = 1 and y = 3 is a solution to the equation for line j: y = ax + 10
Plug in those x- and y-values to get: 3 = a(1) + 10
So, we have: 3 = a + 10, which means
a = -7We're also told that the point (1, 3) lies on line k
So, it must be the case that x = 1 and y = 3 is a solution to the equation for line k: y = bx + a
Plug in those x- and y-values to get: 3 = b(1) + a
Since we now know that
a = -7, we can write: 3 = b(1) +
(-7)We get: 3 = b - 7
Solve: b = 10
Answer: 10
Cheers,
Brent