1. ## [SOLVED] translation

Hi, i have attached a graph i made. Sorry for the sloppy graph cuz it was my first time using the software, and don't mind the little box in the top right hand corner. I don't get how to get rid of it. Also the red line with the two set of points in line L

Here's the question:
The figure shows line L in the xy-coordinate plane. Line m (not shown) is obtained by horizontally translating each point on line L 2 units to the left. if the equation of m is (4/5)x+k. what value is k?

2. Originally Posted by fabxx
Here's the question:
The figure shows line L in the xy-coordinate plane. Line m (not shown) is obtained by horizontally translating each point on line L 2 units to the left. if the equation of m is (4/5)x+k. what value is k?
Value of m line is $\displaystyle m=\frac{4}{5}*(x+2) + k'$. So the k' value (let k be of L line) is $\displaystyle k'=k+\frac{4}{5}*2$. Just cue visually moving the L line towards left.

Look at the point where the L line crosses the y-axis (it's a 4, right?). This is your $\displaystyle k$.
Now, if you move your L line to left (just horizontally) you can imagine that the point (where it crosses the axis) goes "up", right? Moving it for 2 units to left gives you new crossing point $\displaystyle k' = k + 2*\frac{4}{5} = 4 + 2*\frac{4}{5} = \frac{20}{5}+2*\frac{4}{5}=\frac{20}{5}+\frac{8}{5 }=\frac{28}{5}$