Question

Two lines defined by the equations $y = mx + 4$ and $y = 3x + b$, where $m$ and $b$ are constants, intersect at the point $(6, 10)$. What is the value of $b + m$?

Answer 1

-7

Explanation:

The two lines intersect at the point (6,10), so this point belongs to both lines. This means that if we use the value of x = 6 in the lines, we will find y = 10

So we can use this point to find the values of b and m:

y = mx + 4

10 = 6m + 4

6m = 6

m = 1

y = 3x + b

10 = 3*6 + b

b = 10 - 18 = -8

So the value of b + m is -8 + 1 = -7