After finding the equation of the line, it is found that:
Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear equation.
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Equation of a line:
The equation of a line is given by:
[tex]y = mx + b[/tex]
In which m is the slope and b is the y-intercept.
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Finding the slope:
Given two points (x,y), the slope is given by change in y divided by change in x.
- Points (3,6) and (5,12)
- Change in y: 12 - 6 = 6
- Change in x: 5 - 3 = 2
- Slope: [tex]m = \frac{6}{2} = 3[/tex]
Thus:
[tex]y = 3x + b[/tex]
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To find the y-intercept, we replace one of the points into the equation. I will replace (3,6). Thus:
[tex]6 = 3(3) + b[/tex]
[tex]b = 6 - 9 = -3[/tex]
Thus, the equation of the line is:
[tex]y = 3x - 3[/tex]
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Is (4,8) a solution of the same linear equation?
We have to replace x by 4 and y by 8, and see if it results in an identity. So
[tex]8 = 3(4) - 3[/tex]
[tex]8 = 12 - 3[/tex]
[tex]8 \neq 9[/tex]
Since replacing x by 4 and y by 8 in the equation of the line does not result in an identity, (4,8) is not a solution of the same linear equation.
A similar problem is given at https://brainly.com/question/16024991
