Question

Write the equation of the line parallel to the given line and passing through the given point.

Answer 1

Answer:

  a)  y = 2x +4

  b)  y = 1/2x +4

  c)  y = -2x +11

Step-by-step explanation:

The given equations are in slope-intercept for, so we can read the slope directly from the equation. It is the x-coefficient.

We can then write an equation of a parallel line using the point-slope form of the equation of a line:

  y -k = m(x -h) . . . . for a line with slope m through point (h, k)

If you like, you can rearrange this to "slope-intercept" form. Add k and simplify.

  y = mx +(k -mh)

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a) m = 2, (h, k) = (3, 10)

  y = 2x +(10 -2·3)

  y = 2x +4

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b) m = 1/2, (h, k) = (0, 4)

  y = 1/2x +(4 -(1/2)·0)

  y = 1/2x +4

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c) m = -2, (h, k) = (4, 3)

  y = -2x +(3 -(-2)(4))

  y = -2x +11