Which equation could have been used to create this table?
2 answers:
Answer:
y = 3x
Step-by-step explanation:
(1,3) (2,6)
The first step is to find the rate of change ( or slope)
m = (y2-y1)/(x2-x1)
m = (6-3)/(2-1)
m = 3/1
m = 3
Then we need to use the point slope form of the equation of a line
y-y1 = m(x-x1)
y-3 = 3(x-1)
Distribute the 3
y-3 = 3x-3
Add 3 to each side
y-3+3 = 3x-3+3
y = 3x
The slope-intercept form:
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
m - slope
b - y-intercept
The formula of a slope:
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
We have the points (1, 3) and (2, 6). Substitute:
![m=\dfrac{6-3}{2-1}=\dfrac{3}{1}=3](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B6-3%7D%7B2-1%7D%3D%5Cdfrac%7B3%7D%7B1%7D%3D3)
Therefore we have:
![y=3x+b](https://tex.z-dn.net/?f=y%3D3x%2Bb)
Put the coordinates of the point (1, 3) to the equation and calculate a value of b:
![3=3(1)+b](https://tex.z-dn.net/?f=3%3D3%281%29%2Bb)
<em>subtract 3 from both sides</em>
![0=b\to b=0](https://tex.z-dn.net/?f=0%3Db%5Cto%20b%3D0)
<h3>Answer: y = 3x + 0 = 3x</h3>
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