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

4 puzzles in 3 hours

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Answer from: Quest

41*67/2=1373.5

step-by-step explanation:

i just used a calculator

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