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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 AB?

Sagot :

sqdancefan

Answer:

  y = -5/3x   or   5x +3y = 0

Step-by-step explanation:

To write the equation of a line through the origin, we need only find its slope. It is parallel to the line through the given points, so will have the same slope.

Slope

The slope of a line through points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

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

Equation

The line trough the origin has a y-intercept of zero, so its equation will be ...

  y = mx

For the slope we found, the desired equation is ...

  y = -5/3x

Standard form

If we multiply by 3 and add 5x, we have ...

  3y = -5x

  5x +3y = 0 . . . . . . standard form equation of the line

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