Question

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

a)
y=2x−8 through (3,10)
b)
y= 1/2 x+2 through (0,4)
c)
y=−2x−1 through (4,3)

Answer 1

a) y = 2x +4

b) y = 1/2x +4

c) y = -2x +11

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)

__

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

y = 2x +(10 -2·3)

y = 2x +4

__

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

y = 1/2x +(4 -(1/2)·0)

y = 1/2x +4

__

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

y = -2x +(3 -(-2)(4))

y = -2x +11