Expert: Abe Mantell - 5/30/2009

Question
we are doing co-ordinates of the points on a line graph.I an a little confused. The question is
The points (1,3),(2,5),(8,17),(50<101),and (1000,2001) all lie on line M.
The points(1,1),(2,3),(8,negative15),(59,negative99)and(1000,negative1999)all lie on line N.
a.form the equations of both the lines.show you work
b.What are the co-ordinates of the point of intersetion of lines M and N?
c.write the co-ordinates of the intersections of lines M and N with x-axis.
d.Write the co-ordinates of the intersections of lines M and N the y- axis.
And she told me to use this formula for this problem (y-y1)=m(x-x1) and the x and the y are left as variables.Math is really hard for me.These are homework problems.

Answer
Hello Sabrina,

a) All we need are two points to determine a line.  Let's use the
- the first two: (1,3) & (2,5)...find the slope: m=(5-3)/(2-1)=2
- Now use the formula (y-y1)=m(x-x1) ==> y-3=2(x-1) ==> y-3=2x-2
- so the equation is: y=2x+1, and you can verify all the other points
- also check out.
- for the other line, let's use (1,1) & (2,3)...slope, m=(3-1)/(2-1)=2
- so y-1=2(x-1) ==> y-1=2x-2 ==> so the equation is y=2x-1

b) Set them "equal to each other" to determine where they intersect.
- thus 2x+1=2x-1 gives 1=-1, which is impossible, so they do not
- intersect (since they are parallel).

c) x-intercepts are where y=0...
- for M: 2x+1=0 ==> x=-1/2
- for N: 2x-1=0 ==> x=1/2

d) y-intercepts are where x=0...
- for M: y=+1
- for N: y=-1

I hope this helps!  Enjoy!!  :-)

Abe