Question 153151
1.	How do we write the equation of a horizontal line?  What would be an example?


The equation of a horizontal line does not have an x term.  So therefore, y=mx+b becomes y=b.  Set a value for b, such as y=3, and there you have it.


2.	How do we write the equation of a vertical line?  What would be an example? 


This is just like a horizontal line, only there is no y value.   So like y=b, you would just have x=b.  once again, set a value for b, such as x=2, and there you have it.



3.	The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M.
The points (3, -9), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240) all lie on line N.
a.	Form the equations of both the lines.  Show your work.  


First get the slopes.  slope equals the change in y over the change in x.  So just grab any two coordinates of each line and plug in the y and x values.  Let's use the easiest:


Line M:   3-5/9-13=-2/-4 or 1/2
So y=mx+b becomes y=1/2x+b
Plug in coordinates again,
3=1/2(9)+b


Solve
3=4.5+b
-1.5=b


~~~y=1/2x-3/2----------------Line M~~~


Line N:   3-5/-9--11=-2/2 or -1
y=-x+b


Plug in coordinates
3=-(-9)+b
3=9+b


Solve
-6=b


~~~y=-x-6--------------------------Line N~~~


b.	What are the co-ordinates of the point of intersection of lines M and N?


You must solve the system of:


y=1/2x-3/2
y=-x-6


Set the values equal to each other
-x-6=1/2x-3/2


Solve
-1/2x-6=-3/2
-1/2x=9/2
x=9


Plug in x to get y.
y=-x-6
y=-9-6
y=-15


(9,-15)


c.	Write the co-ordinates of the intersections of lines M and N with the x-axis.


(9,-15)--------------------------9 is x.


d.	Write the co-ordinates of the intersection of lines M and N with the y-axis. 


(9,-15)------------------------- -15 is y.