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kotegsom [21]
3 years ago
9

Explain how you determine an equation for a line using a table of input/output values.

Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
6 0
Example :

            x               y
            1               3
            2               6
            3               9
            4               12

first thing u do is pick any 2 points (x,y) from ur table

(1,3) and (2,6)
now we sub those into the slope formula (y2 - y1) / (x2 - x1) to find the slope
(y2 - y1) / (x2 - x1)
(1,3)....x1 = 1 and y1 = 3
(2,6)...x2 = 2 and y2 = 6
sub
slope = (6 - 3) / (2 - 1) = 3/1 = 3

now we use slope intercept formula y = mx + b
y = mx + b
slope(m) = 3
use any point off ur table...(1,3)...x = 1 and y = 3
now we sub and find b, the y int
3 = 3(1) + b
3 = 3 + b
3 - 3 = b
0 = b

so ur equation is : y = 3x + 0....which can be written as y = 3x...and if u sub any of ur points into this equation, they should make the equation true....if they dont, then it is not correct

and if u need it in standard form..
y = 3x
-3x + y = 0
3x - y = 0 ...this is standard form
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Irina18 [472]

Answer:

(y-7)^2+(x-2)^2=16

and

(x+2)^2+(y-15)^2 = 9

Step-by-step explanation:

The standard equation of a circle is (x-h)^2+(y-k)^2=r^2 where the coordinate (h,k) is the center of the circle.  

Second Problem:

  1. We can start with the second problem which uses this info very easily.
  2. (h,k) in this problem is (-2,15) simply plug these into the equation. (x--2)^2+(y-15)^2=r^2 .
  3. We can also add the radius 3 and square it so it becomes 9. The equation.
  4. This simplifies to (x+2)^2+(y-15)^2 = 9.

First Problem:

  1. The first problem takes a different approach it is not in standard form. But we can convert it to standard form by completing the square.
  2. y^2-14y+x^2-4x+37=0 first subtract 37 from both sides so the equation is now y^2-14y+x^2-4x=-37.
  3. y^2-14y+x^2-4x+37=0 by adding (-\frac{b}{2a} )^2 to both the x and y portions of this equation you can complete the squares. (-\frac{b}{2a})^2=(-\frac{-14}{2(1)})^2 and (-\frac{-4}{2(1)})^2 which equals 49 and 4.
  4. Add 49 and 4 to both sides and the equation is now:y^2-14y+49+x^2-4x+4=-37+49+4 You can simplify the y and x portions of the equations into the perfect squares or factored form (y-7)^2 and (x-2)^2.
  5. Finally put the whole thing together. (y-7)^2+(x-2)^2=16.

I hope this helps!

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