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through (8,13) paralelo to 7x+8y=88

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2 Answers

We will use three forms of linear equation:
(1) Standard form: Ax + By = C
(2) Slope-intercept form:  y = mx +b
(3) Point-slope form:  y - y1 = m(x - x1)
~~~~~~~
Parallel lines have the same slope. therefore, we have to convert given equation from standard to slope-intercept form:
  7x + 8y = 88
- 7x         - 7x

  8y = -7x + 88
÷8     ÷8    ÷8

y = (-7/8) x + 11 ---> m = (-7/8)

To find the equation of the parallel line, let's use point-slope form:

y - 13 = (-7/8)(x - 8)
y - 13 = (-7/8) x + 7
   +13                + 13

y = (-7/8) x + 20

f(x) = (-7/8) x + 20   <---- final answer.

Function notation is simply replacing y with f(x), g(x), h(x), and so on. 

f(x) = -0.875x + 11

g(8) = 13 = -0.875(8) + c = -7 + c

c = 13 + 7 = 20

Parallel Line: g(x) = -0.875x + 20

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