SOLUTION: HERE ARE SOME SOLUTIONS OF LINE A (3,3) (5,)(15,15) (34,34)(678,678) (1234,1234) SOLUTIONS OF LINE B are: (3,-3) (5,-5) (15,-15)(34,-34)(678,-678) (1234,-1234) a. form the equat

Algebra ->  Linear-equations -> SOLUTION: HERE ARE SOME SOLUTIONS OF LINE A (3,3) (5,)(15,15) (34,34)(678,678) (1234,1234) SOLUTIONS OF LINE B are: (3,-3) (5,-5) (15,-15)(34,-34)(678,-678) (1234,-1234) a. form the equat      Log On


   

Question 112035: HERE ARE SOME SOLUTIONS OF LINE A (3,3) (5,)(15,15) (34,34)(678,678) (1234,1234)
SOLUTIONS OF LINE B are: (3,-3) (5,-5) (15,-15)(34,-34)(678,-678) (1234,-1234)
a. form the equations of both line
b. what are the co-ordinates of the point of intersection of lines a and b?
c. write the co-ordinates of the intersections of lines a and b ith the x-axis
d. write the co-ordinates of the intersection of lines a and b with the y-axis
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
SOLUTIONS OF LINE A+(3,3) (5,)(15,15) (34,34)(678,678) (1234,1234)
SOLUTIONS OF LINE B are: (3,-3) (5,-5) (15,-15)(34,-34)(678,-678) (1234,-1234)
a. form the equations of both line
We need two+points to find equation of line:

Line A
to find equation of form y=+mx+%2B+b, where m is slope, and b is intercept, which passes through points (x%5B1%5D, y%5B1%5D) = (3, 3) and (x%5B2%5D, y%5B2%5D) = (15, 15), we need to calculate a slope m
Slope m is:
+m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29+,
+m+=+%2815+-+3%29%2F%2815+-+3%29+,
m+=+12%2F12
m+=+1


Intercept is found from equation:
mx%5B1%5D+%2B+b+=+y%5B1%5D……move mx%5B1%5Dto the right
+b+=+y%5B1%5D+-+mx%5B1%5D
+b+=+3+-+1%2A3
+b+=+3+-+3

+b+=+0+
Then, your equation is:
y=%281%29x+%2B+%280%29
or
y+=++x+

Line B
to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (3, -3) and (x2, y2) = (5, -5), we need to calculate a slope m
Slope m is:
+m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29+,
+m+=+%28-5+-+%28-3%29%29%2F%285+-+3%29+,
m+=+%28-5+%2B+3%29%2F2
m+=+-2%2F2
m+=+-+1


Intercept is found from equation:
mx%5B1%5D+%2B+b+=+y%5B1%5D……move mx%5B1%5Dto the right
+b+=+y%5B1%5D+-+mx%5B1%5D+
+b+=+-3+-+%28-1%2A3%29+
+b+=+-3+-+%28-3%29+
+b+=+-3+%2B+3+
+b+=+0+
Then, your equation is:
y=%28-1%29x+%2B+%280%29
or
y+=+-+x+


b. the co-ordinates of the+point+of+intersection of lines a and b
are : (0,0)

c. the co-ordinates of the intersections of lines a and b with the x-axis are (0,0)

d. the co-ordinates of the intersection of lines+a and b with the y-axis are (0,0)

Solved by pluggable solver: Solve the System of Equations by Graphing



Start with the given system of equations:


1x%2By=0

-x%2By=0





In order to graph these equations, we need to solve for y for each equation.




So let's solve for y on the first equation


1x%2By=0 Start with the given equation



1y=0-x Subtract +x from both sides



1y=-x%2B0 Rearrange the equation



y=%28-x%2B0%29%2F%281%29 Divide both sides by 1



y=%28-1%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=-x%2B0 Reduce



Now lets graph y=-x%2B0 (note: if you need help with graphing, check out this solver)



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B0%29+ Graph of y=-x%2B0




So let's solve for y on the second equation


-x%2By=0 Start with the given equation



1y=0%2Bx Add +x to both sides



1y=%2Bx%2B0 Rearrange the equation



y=%28%2Bx%2B0%29%2F%281%29 Divide both sides by 1



y=%28%2B1%2F1%29x%2B%280%29%2F%281%29 Break up the fraction



y=x%2B0 Reduce





Now lets add the graph of y=x%2B0 to our first plot to get:


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+-x%2B0%2Cx%2B0%29+ Graph of y=-x%2B0(red) and y=x%2B0(green)


From the graph, we can see that the two lines intersect at the point (0,0) (note: you might have to adjust the window to see the intersection)