SOLUTION: The following table of values represents points (x, y) on the graph of a linear function. Determine the y-intercept of this graph. x y -2 8 1 2 2 0 4 -4

Algebra ->  Linear-equations -> SOLUTION: The following table of values represents points (x, y) on the graph of a linear function. Determine the y-intercept of this graph. x y -2 8 1 2 2 0 4 -4      Log On


   

Question 1160169: The following table of values represents points (x, y) on the graph of a linear function. Determine the y-intercept of this graph.
x y
-2 8
1 2
2 0
4 -4
Found 3 solutions by MathLover1, greenestamps, josgarithmetic:
Answer by MathLover1(20849) About Me  (Show Source):
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The following table of values represents points (x,+y) on the graph of a linear function. Determine the y-intercept of this graph.
+x++y
-2++8
+1+ 2
2++0
+4+-4
first find equation using point slope formula:

y-y%5B1%5D=m%28x-x%5B1%5D%29
to find a slope, use two given points:
-2++8
+1+ 2
m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29
m=%282-8%29%2F%281-%28-2%29%29
m=-6%2F%281%2B2%29
m=-6%2F3
m=-2

y-y%5B1%5D=m%28x-x%5B1%5D%29, plug in slope m=-2 and coordinates of point 2++0
y-0=-2%28x-2%29
y=-2x%2B4-> your equation

to find y-intercept, set x=0
y=-2%2A0%2B4
y=4

y-intercept is at (0,4)









Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Solving the problem using formal algebra, as the other tutor did, is something a student should know how to do, especially if he is just beginning to study algebra.

But using your understanding of linear functions to solve the problem using logical reasoning can be a valuable exercise in learning.

We want to find the y-intercept, which is the point where the graph crosses the y-axis -- i.e., where the x value is 0.

Look at the two points A(2,0) and B(1,2). To get from A to B, we move 1 unit to the left and 2 units up. Since the function is linear, when we again move 1 unit left and 2 units up we will be at another point on the graph.

But 1 unit left and 2 units up from B(1,2) puts us at (0,4) -- and that's exactly where we want to be.

So the y-intercept is (0,4).

Students will like math a lot more if they think about what the formal formulas are telling you -- instead of just doing rote memorization of the formulas and applying them without thinking about what they mean.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
   x     y
  -2     8
   1     2
   2     0
   4    -4



Assuming the (x,y) points are on a line, then looking closer at these:
  x     y
  -2    8

  0     ?

  1     2

Distance d from "?" to 8 ;
d%2F%280-%28-2%29%29=%288-2%29%2F%281-%28-2%29%29
d%2F2=6%2F3
d%2F2=2
d=4
The missing y-value is 8-d=8-4=4;
The y-intercept is (0,4).