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[\overleftrightarrow?]AB passes through A(-3, 0) and B(-6, 5). What is the equation of the line that passes through the origin and is parallel to
[loverleftrightarrow?] AB?
OA 5x-3y=0
OB. -x+3y=0
OC. -5x-3y=0
OD. 3x+5y=0
OE. -3x+ 5y=0

Respuesta :

The linear equation that passes through the origin and is parallel to AB is given by:

C. -5x - 3y = 0.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

When two lines are parallel they have the same slope, which is given by change in y divided by change in x, hence:

m = (5 - 0)/(-6 - (-3)) = -5/3

It goes through the origin, that is, the y-intercept is b = 0, hence the equation is:

[tex]y = -\frac{5}{3}x[/tex]

5x + 3y = 0.

C. -5x - 3y = 0.

More can be learned about linear equations at https://brainly.com/question/24808124

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