dave13 wrote:
manishuol wrote:
In the coordinate plane, points (x, 1) and (10, y) are on line k. If line k passes through the origin and has slope 1/2, then x + y =
(A) 4.5
(B) 7
(C) 8
(D) 11
(E) 12
Hi
niks18 please let me know if my solution/ approach is correct ?
\(\frac{1-y}{x-10}=\frac{1}{2}\) cross multiply
\(2-2y = x-10\)
\(x-10-2+2y\)
\(x+2y-12 = 0\)
\(2y= 12-x\)
\(
y = \frac{-x}{2}+ 6\)
now since I know that slop is \(1/2\) hence x = 1 and y intercept is 6 so x+y = 1+6 = 7
Answer: 7 <---- :)
many thanks! :)
Hi
dave13,
what you have done is used the formula to find slope and converted it to an algebraic equation which does not represent the equation of line.
equation of line is \(y=mx+c\), where \(m\) is slope of the line
as per your equation \(y=\frac{-1}{2}x+6\), so here slope, \(m=\frac{-1}{2}\) which is incorrect.
We know that the line passes through the origin so our equation should be
\(y=\frac{1}{2}x+c\) and at origin we have (0,0)
so \(0=\frac{1}{2}*0+c => c=0\) i.e y-intercept is 0 (as per your equation y intercept is 6 which is incorrect). If a line passes through origin it will not cut y-axis and hence there will be no intercept.
Hence equation of line will be \(y=\frac{1}{2}x\)
now at (x,1) we will have \(1=\frac{1}{2}x=>x=2\)
and at (10,y) we will have \(y=\frac{1}{2}*10 =>y=5\)
Hence \(x+y=2+5=7\)
There is an alternate method as well using only the formula to find slope. This method is also explained in earlier posts.