Question

A construction crew will build a new railroad track which passes through the point (8,5) and is parallel to the one

modeled by the line. What equation models the path of the new track?

Answer 1

y =
`-(2)/(9)x+(61)/(9)`

Explanation:

Let the equation of the new railroad track passing through the point
`(x_1,y_1)` and slope = m₁ is,

`y-y_1=m_1(x-x_1)`

Slope of the given line =
`(y_2-y_1)/(x_2-x_1)`

Slope of the line passing through (-3, 1) and (6, -1) will be,

m₂ =
`(1+1)/(-3-6)`

m₂ =
`-(2)/(9)`

Since, railroad track and the given line are parallel,

m₁ = m₂ =
`-(2)/(9)`

Therefore, equation of the railroad track passing through (8, 5) and slope =
`-(2)/(9)` will be,

y - 5 =
`-(2)/(9)(x-8)`

y =
`-(2)/(9)x+(16)/(9)+5`

y =
`-(2)/(9)x+(61)/(9)`