Mathematics, 15.07.2019 23:00 rosehayden21

Which table represents a linear function?

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Answer from: alvalynnw

Table-1 represents a linear function.

Further explanationA line that is not parallel to either the x-axis or the y-axis represents a line that occupies a slope or in other words a gradient.The gradient or steepness of a straight line is the rate at which the line rises or falls. The gradient is the same at any point along a straight line. The symbol m is used to represent the gradient or slope.

In general, the gradient of the line joining the points A(x₁, y₁) and B(x₂, y₂) is given by the formula:

$\boxed{\boxed{ \ m = \frac{y_2 - y_1}{x_2 - x_1} \ }}$

Let's examine the slope (m) of each table.

Table-1: (1, 3), (2, 7), (3, 11), (4, 15)

(1, 3) and (2, 7) ⇒ $m = \frac{7-3}{2-1} = 4$

(2, 7) and (3, 11) ⇒ $m = \frac{11-7}{3-2} = 4$

(3, 11) and (4, 15) ⇒ $m = \frac{15-11}{4-3} = 4$

or, we choose (1, 3) and (4, 15) ⇒ $m = \frac{15-3}{4-1} = 4$

Because it has the same slope of m = 4, this table represents a linear function.

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Table-2: (1, 3), (2, 8), (3, 15), (4, 21)

(1, 3) and (2, 8) ⇒ $m = \frac{8-3}{2-1} = 5$

(2, 8) and (3, 15) ⇒ $m = \frac{15-8}{3-2} = 7$

Because it does not have the same slope, this table does not represent a linear function.

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Table-3: (1, 3), (2, 9), (3, 3), (4, 9)

(1, 3) and (2, 9) ⇒ $m = \frac{9-3}{2-1} = 6$

(2, 9) and (3, 3) ⇒ $m = \frac{3-9}{3-2} = -6$

Because it does not have the same slope, this table does not represent a linear function.

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Table-4: (1, 3), (2, 9), (3, 27), (4, 81)

(1, 3) and (2, 9) ⇒ $m = \frac{9-3}{2-1} = 6$

(2, 9) and (3, 27) ⇒ $m = \frac{27-9}{3-2} = 18$

Because it does not have the same slope, this table does not represent a linear function.

Based on the pattern shown in Table-4, the curve represents the function of $\boxed{y = 3^x}$ .

Consider the proof below:

$x = 1 \rightarrow y = 3^1 = 3$ $x = 2 \rightarrow y = 3^2 = 9$ $x = 3 \rightarrow y = 3^3 = 27$ $x = 4 \rightarrow y = 3^4 = 81$ Learn moreFinding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point The midpoint Find the missing endpoint if the midpoint is known

Keywords: which table, represents, a linear function, gradient, slope, rate, straight, points, the formula, m = 4

Answer from: Quest

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes.

step-by-step explanation:

Answer from: Quest

29 mil

step-by-step explanation: