Question

Question #c8b37

Answer 1

`g(x) = -1/3x + 7/3`

Explanation:

Two lines `y = m_1x+b_1` and `y = m_2x+b_2` are perpendicular if and only if `m_1 = -1/m_2`

As we wish for `g(x)` to be perpendicular to a line with slope `3`, we know that `g(x)` has a slope of `-1/3`. As we are also given that `g(x)` passes through the point `(1, 2)`, we can plug these into the point-slope form of a line: `y - y_1 = m(x-x_1)` to get the graph `y = g(x)` as

`y-2 = -1/3(x-1)`

`=> y-2 = -1/3x + 1/3`

`=> y = -1/3x + 7/3`

`:. g(x) = -1/3x + 7/3`