The points (3,6) and (5,12) lie on the graph of a linear equation. Is (4,8) a solution of the same linear equation? Explain.

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:

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.

Thus:

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To find the y-intercept, we replace one of the points into the equation. I will replace (3,6). Thus:

Thus, the equation of the line is:

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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

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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