## Which table represents a linear function?

Question

Which table represents a linear function? in progress 0

1. Well, a linear function is proportional, a straight line (on a graph). And the numbers must not have the same answer. For instance, if the X input is 5, and the Y output is 7. And then another X input is 5, and the Y output is 8, that’s non-linear.

So, the Answer would be the third graph. This is because the X values are steadily increasing, and so are the Y values.

For the X and Y values, for each time X increases by 1, Y increases by -8. This is, linear because both sides are constantly and evenly increasing.

2. Table 3 represents the linear function.n

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Further explanation:n

The linear equation with slope m and intercept c is given as follows.n

[tex]boxed{y = mx + c}[/tex]

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The formula for slope of line with points [tex]left( {{x_1},{y_1}} right)[/tex] and [tex]left( {{x_2},{y_2}} right)[/tex] can be expressed as,n

[tex]boxed{m = frac{{{y_2} – {y_1}}}{{{x_2} – {x_1}}}}[/tex]

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Explanation:n

In table 1,n

The slope can be obtained as follows,n

[tex]begin{aligned}m&=frac{{ – 6 + 2}}{{2 – 1}}&=frac{{ – 4}}{1}&= – 4end{aligned}[/tex]

The slope of other two points can be obtained as follows,n

[tex]begin{aligned}m&= frac{{ – 2 + 6}}{{3 – 2}}&= frac{4}{1}&=4end{aligned}[/tex]

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The slope is not equal. Therefore, table 1 is not correct.n

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In table 2,n

The slope can be obtained as follows,n

[tex]begin{aligned}m&= frac{{ – 5 + 2}}{{2 – 1}}&=frac{{ – 3}}{1}&= – 3end{aligned}[/tex]

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The slope of other two points can be obtained as follows,n

[tex]begin{aligned}m&=frac{{ – 9 + 5}}{{3 – 2}}&= frac{{ – 4}}{1}&= – 4end{aligned}[/tex]

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The slope is not equal. Therefore, table 2 is not correct.n

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In table 3,n

The slope can be obtained as follows,n

[tex]begin{aligned}m&= frac{{ – 10 + 2}}{{2 – 1}}&= frac{{ – 8}}{1}&= – 8end{aligned}[/tex]

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The slope of other two points can be obtained as follows,n

[tex]begin{aligned}m&= frac{{ – 18 + 10}}{{3 – 2}}&= frac{{ – 8}}{1}&= – 8end{aligned}[/tex]

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The slopes are equal. Therefore, table 3 is correct.n

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In table 4,n

The slope can be obtained as follows,n

[tex]begin{aligned}m&= frac{{ – 4 + 2}}{{2 – 1}}&=frac{{ – 2}}{1}&= – 2end{aligned}[/tex]

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The slope of other two points can be obtained as follows,n

[tex]begin{aligned}m&=frac{{ – 8 + 4}}{{3 – 2}}&= frac{{ – 4}}{1}&= – 4end{aligned}[/tex]

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The slope is not equal. Therefore, table 4 is not correct.n

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Table 3 represents the linear function.n

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