SOLUTION: Write an equation of the line with these conditions: 2,5 slope 3 -3-1 slope 1/2 (-3,4), (1,12) (-1,6) (2,4) (2,1) slope 0

Algebra ->  Graphs -> SOLUTION: Write an equation of the line with these conditions: 2,5 slope 3 -3-1 slope 1/2 (-3,4), (1,12) (-1,6) (2,4) (2,1) slope 0      Log On


   

Question 995091: Write an equation of the line with these conditions:
2,5 slope 3
-3-1 slope 1/2
(-3,4), (1,12)
(-1,6) (2,4)
(2,1) slope 0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
here you need to use slope-intercept form of equation of the line: y=mx%2Bb where m is the slope and b is y-intercept
use given point (2,5) and slope m=3 to find y-intercept b

so,we have
5=3%2A2%2Bb
5=6%2Bb
5-6=b
b=-1
so, your equation is: y=3x-1


for
(-3,-1) and slope m=1%2F2
we have
-1=%281%2F2%29%2A%28-3%29%2Bb
-1=-3%2F2%2Bb
-1%2B3%2F2=b
-2%2F2%2B3%2F2=b
b=1%2F2
equation is: y=%281%2F2%29x%2B1%2F2



for
(-3,4), (1,12)
we have
4=m%2A%28-3%29%2Bb
4=-3m%2Bb.........eq.1
12=m%2A%281%29%2Bb
12=m%2Bb.........eq.2
subtract eq.1 from eq.2
12-4=m%2Bb-%28-3m%2Bb%29
8=m%2Bcross%28b%29%2B3m-cross%28b%29
8=4m
m=2
go to 4=-3m%2Bb.........eq.1 substitute 2 for m and solve for b
4=-3%2A2%2Bb
4=-6%2Bb
4%2B6=b
b=10
equation is: y=2x%2B10



for
(-1,6) (2,4)
6=m%2A%28-1%29%2Bb
6=-m%2Bb.........eq.1
4=m%2A%282%29%2Bb
4=2m%2Bb.........eq.2
-------------------
6-4=-m%2Bb-%282m%2Bb%29
2=-m%2Bb-2m-b
2=-3m
m=-2%2F3
4=2%28-2%2F3%29%2Bb.........eq.2
4=%28-4%2F3%29%2Bb
4%2B4%2F3=b
12%2F3%2B4%2F3=b
16%2F3=b
equation is: y=-%282%2F3%29x%2B16%2F3



for
(2,1) and slope m=0
1=0%2A%282%29%2Bb
b=1

equation is: y=1 (horizontal line)