SOLUTION: I was told to write the slope-intecept form of the equation for the line. Then I was given a graph and 4 choices for my answer. The graph has points at (3,0) and (-3,-2) the slop

Algebra ->  Linear-equations -> SOLUTION: I was told to write the slope-intecept form of the equation for the line. Then I was given a graph and 4 choices for my answer. The graph has points at (3,0) and (-3,-2) the slop      Log On


   

Question 367342: I was told to write the slope-intecept form of the equation for the line. Then I was given a graph and 4 choices for my answer. The graph has points at (3,0) and (-3,-2) the slope I think is 3
Found 3 solutions by jim_thompson5910, rfer, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=3 and y%5B1%5D=0.
Also, is the second point . So this means that x%5B2%5D=-3 and y%5B2%5D=-2.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%28-2-0%29%2F%28-3-3%29 Plug in y%5B2%5D=-2, y%5B1%5D=0, x%5B2%5D=-3, and x%5B1%5D=3


m=%28-2%29%2F%28-3-3%29 Subtract 0 from -2 to get -2


m=%28-2%29%2F%28-6%29 Subtract 3 from -3 to get -6


m=1%2F3 Reduce


So the slope of the line that goes through the points and is m=1%2F3


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-0=%281%2F3%29%28x-3%29 Plug in m=1%2F3, x%5B1%5D=3, and y%5B1%5D=0


y-0=%281%2F3%29x%2B%281%2F3%29%28-3%29 Distribute


y-0=%281%2F3%29x-1 Multiply


y=%281%2F3%29x-1 Simplify




So the equation that goes through the points and is y=%281%2F3%29x-1


Notice how the graph of y=%281%2F3%29x-1 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F3%29x-1 through the points and

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

Answer by rfer(16322) About Me  (Show Source):
You can put this solution on YOUR website!
slope m=3
y=3x-1

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I was told to write the slope-intecept form of the equation for the line. Then I was given a graph and 4 choices for my answer. The graph has points at (3,0) and (-3,-2) the slope I think is 3
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The slope is diffy/diffx = -2/-6
slope m = 1/3
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Do it like this:
Given 2 points example.
Find the equation of the line thru the points (2,1) and (3,5)
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This is a 2 step process. First find the slope of the line thru the points.
slope, m = diffy/diffx
m = (5-1)/(3-2)
m = 4
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Now use y = mx + b with either point to find b, the y-intercept.
y = mx + b
5 = 4*3 + b
b = -7
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y = mx + b
y = 4x - 7 is the answer.
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Another approach using determinants:
|x y 1|
|2 1 1| = 0
|3 5 1|
--------
x(1-5) - y(2-3) + 1(10-3) = 0
-4x + y + 7 = 0
y = 4x - 7
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