Pieces of a Mystery Line
Consider two lines If a third line has the same slope as the first line and passes through the -intercept of the second line, what is ?
The answer is 4.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
We rewrite the equation of the first line to obtain 9 x + 4 y + 1 = 0 ⇒ y = − 4 9 x − 4 1 ⇒ m = − 4 9 .
To obtain the x -intercept of the second line, we substitute y = 0 and solve for x : 4 x + 1 5 ⋅ 0 + 1 6 = 0 ⇒ x = − 4 . This implies that the third line y = m x + b = − 4 9 x + b passes through point ( − 4 , 0 ) . Thus, we substitute x = − 4 and y = 0 to obtain 0 = − 4 9 ⋅ ( − 4 ) + b ⇒ b = − 9 ⇒ m b = ( − 9 ) ⋅ ( − 9 4 ) = 4 .