It seems that solution of Question #7 Chapter 5 Geometry book is incorrect.

Q - a line has a slope of 3/4 and intersects the point(12,-39). at which point does this line intersect the x-axis?

Solution:
y = 3/4x + b

-39 = (3/4)* (-12) + b

It should be +12 and not -12 so final answer would be (64,0) and not (40,0).

-Pathik

Solution: y = 3/4x + b
-39 = (3/4)* (12) + b
so b = - 48

the point at x axis is (x, y) where the value of x is unknown and y has to be 0. so our equation becomes

0 = (3/4) x - 48
x = 64

you two are correct.

here's another, perhaps faster, way of thinking about it:

we know that slope is equal to rise/run, or (change in y)/(change in x)
...and, in this problem, we know that the 'change in y' must be equal to +39 if we're going to get to the x-axis (where the y-value is 0).

therefore
(change in y)/(change in x) = +39/n = 3/4
n = 52 (you can do this in your head if you know the multiples of numbers like 13: 39 = 3 x 13 and 52 = 4 x 13)

therefore, x must increase by 52 for y to increase by 39.
so
x = 12 + 52 = 64

This has been fixed in the latest printing. The typo is actually in the problem, not the solution! The point should have read (-12, -39), but the negative in front of the 12 got dropped in the first printing. :)