The two lines created from the points (0, 10), (2, 7) and (-3, -3) works
exclusively with the three points as presented in the the attached graph.
<h3>Which methods can be used to obtain linear functions?</h3>
The possible value in the table obtained from a similar question is presented as follows;
![\begin{array}{|lcl|}(-1, \, 1)&&(2, \, 7)\\(-4, \, 8)&&(2, \, 11)\\(0, \, 10)&&(-3, \, -3)\end{array}\right]](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7B%7Clcl%7C%7D%28-1%2C%20%5C%2C%201%29%26%26%282%2C%20%5C%2C%207%29%5C%5C%28-4%2C%20%5C%2C%208%29%26%26%282%2C%20%5C%2C%2011%29%5C%5C%280%2C%20%5C%2C%2010%29%26%26%28-3%2C%20%5C%2C%20-3%29%5Cend%7Barray%7D%5Cright%5D)
A line is defined as the shortest distance between two points.
Taking the points (0, 10) and (-3, -3), we have;
![Slope = \dfrac{10 - (-3)}{0 - (-3)} = \dfrac{13}{3}](https://tex.z-dn.net/?f=Slope%20%3D%20%5Cdfrac%7B10%20-%20%28-3%29%7D%7B0%20-%20%28-3%29%7D%20%3D%20%5Cdfrac%7B13%7D%7B3%7D)
Which gives;
![y -10 = \dfrac{13}{3} \times x](https://tex.z-dn.net/?f=y%20-10%20%3D%20%5Cdfrac%7B13%7D%7B3%7D%20%5Ctimes%20x)
![y = \dfrac{13}{3} \cdot x + 10](https://tex.z-dn.net/?f=y%20%20%3D%20%5Cdfrac%7B13%7D%7B3%7D%20%5Ccdot%20x%20%2B%2010)
From the attached graph, the points (-1, 1), (2, 7), (2, 11), and (-4, 8) are not on the line.
The linear function,
works exclusively for the points (0, 10) and (-3, -3), given that the coordinates of points on the line are; (-1,
), (2,
), (-4,
)
Second line
Taking the points (2, 11) and (-3, -3), we have;
![Slope = \mathbf{\dfrac{11 - (-3)}{2 - (-3)}}= \dfrac{14}{5} = 2.8](https://tex.z-dn.net/?f=Slope%20%3D%20%5Cmathbf%7B%5Cdfrac%7B11%20-%20%28-3%29%7D%7B2%20-%20%28-3%29%7D%7D%3D%20%5Cdfrac%7B14%7D%7B5%7D%20%3D%202.8)
Which gives;
![y - (-3) = 2.8\times (x - (-3)) = 2.8 \cdot x + 8.4](https://tex.z-dn.net/?f=y%20-%20%28-3%29%20%3D%202.8%5Ctimes%20%28x%20-%20%28-3%29%29%20%3D%202.8%20%5Ccdot%20x%20%2B%208.4)
y = 2.8·x + 8.4 - 3 = 2.8·x + 5.4
Which gives;
y = 2.8·x + 5.4
The line, y = 2.8·x + 5.4, works exclusively for the points (2, 11) and (-3, -3), given that the points (2, 7), (2, 11), (0, 10), and (-3, -3) are not on the line
The coordinates of points on the line are; (-1, 2.6), (-4, -5.8), and (0, 5.4).
Learn more about linear functions here:
brainly.com/question/20478559