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Answered

The graph below shows a line segment AB:


Which of the following equations best represents the line segment AB?

graph of line AB going through ordered pairs negative 1, 5 and 2, negative 4


y = −3x + 2

y = −2x + 1

y = −3x − 2

y = −2x − 1

Verified Answer :

nobillionaireNobley

Equation of a line passing through given two points is given by (y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
(y - 5)/(x - (-1)) = (-4 - 5)/(2 - (-1))
(y - 5)/(x + 1) = -9/(2 + 1) = -9/3 = -3
y - 5 = -3(x + 1) = -3x - 3
y = -3x - 3 + 5
y = -3x + 2

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that the line AB, going through ordered pairs (-1,5) and (2,-4).

If a line passing through two points, then the equation of line is

\(y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

The equation of line AB is

\(y-5=\frac{-4-5}{2-(-1)}(x-(-1))\)

\(y-5=\frac{-9}{2+1}(x+1)\)

\(y-5=\frac{-9}{3}(x+1)\)

\(y-5=-3(x+1)\)

\(y-5=-3x-3\)

Add 5 both the sides.

\(y=-3x+2\)

Therefore option 1 is correct.

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