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(2, -4), (x, y) , A , and B all lie on the line. Find an equation relating x and y.​

(2, -4), (x, y) , A , and B all lie on the line. Find an equation relating x and y-example-1
User Web User
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2 Answers

9 votes

Answer:

no

Explanation:

yes

User Brad Folkens
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6 votes

Answer:

An equation relating x and y is:

y = 3/4x - 5.5

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the points

(2, -4), (x, y), A(6, -1), and B(10, 2)

Taking any two points let say A(6, -1), and B(10, 2) to determine the slope


\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)


\left(x_1,\:y_1\right)=\left(6,\:-1\right),\:\left(x_2,\:y_2\right)=\left(10,\:2\right)


m=(2-\left(-1\right))/(10-6)

Refine


m=(3)/(4)

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = -5.5

Thus, the y-intercept b = -5.5

Thus, substituting b = -5.5 and m = 3/4 in the slope-intercept form of the line equation

y = mx+b

y = 3/4x + (-5.5)

y = 3/4x - 5.5

Therefore, an equation relating x and y is:

y = 3/4x - 5.5

User Hey StackExchange
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