A simple Line question

[Mason]

Rani is comparing the monthly costs from two internet service providers. #1 charges $10 initially + $.75 per hour #2 is $5 initially and $1 per hour!

How would i figure when the two lines which i already have in y=mx+b which are y=.75x+10 and y=1x+5. how do i figure out the coordinates without using a graph so algebraicly

[DAiv]

I presume you mean, when do the two lines cross (when do both equations have the same x and y values).

To solve it algebraically, set the first equation equal to the second equation (substitute '.75x + 10' into the y of 'y = x + 5') and solve for x. Then substitute x back into either of the equations to find out y.


DAiv

[little_dragon]

I did this a chapter or two ago. The graphing is so long and boring! Algebraically is faster and easier! Since you have both as "y=", you can just do the two other sides equal to each other: 0.75x + 10 = x + 5. Then minus 0.75 from each side and minus 5 from each side: 5 = 0.25x. 0.25 = 1/4, so times by 4: 20 = x.

You can put 5 in for x in either one of the first equations, and this will give you y.