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Identify which table represents the equation, y = 3x + 2, end it supported with the correct reasoning.

A. table 2 because when finding the slope between (2,8) and (-4,-10) you get 3. then substituting (2,8) in gives you a Y intercept of 2 and this works for all points.

B. both table 1 and 2 work for the equation for all points

C. None, both table 1 and 2 have coordinate points that do not lie on the line of the equation.

D. table 1 because when substituting (-1,-1) it makes both sides of the equation equal and so do the other points in the table.

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jimrgrant1 jimrgrant1 · Answer 1 · 2020-01-15T19:38:07+01:00

Answer:

A

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Table 1

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (5, 11) ← 2 ordered pairs from the table

m = [tex]\frac{11+1}{5+1}[/tex] = [tex]\frac{12}{6}[/tex] = 2, thus

y = 2x + c ← is the partial equation

To find c substitute (5, 11) into the partial equation

11 = 10 + c ⇒ c = 11 - 10 = 1

y = 2x + 1 ← equation representing Table 1

Table 2

let (x₁, y₁ ) = (2, 8) and (x₂, y₂ ) = (- 4, - 10)

m = [tex]\frac{-10-8}{-4-2}[/tex] = [tex]\frac{-18}{-6}[/tex] = 3, thus

y = 3x + c ← is the partial equation

To find c substitute (2, 8) into the partial equation

8 = 6 + c ⇒ c = 8 - 6 = 2

y = 3x + 2 ← equation representing Table 2