If a line t (f(x) = 2x +3) is perpendicular to a line n that passes through point (3,7), what is the equation of line n?

Firstly, we need to think of the equation of a line formula to figure out what information we have been given. y-y1 = m(x-x1) -> (x1, y1)This formula uses a point and a slope. We have been given a point on the line n already, (3, 7).We now must find the slope, m. The question says line t and n are perpendicular to each other, so the slopes must be negatively reciprocal (opposites). The slope of line t is:y = 2x+3 -> y = mx + cm = 2So the slope of n will be -1/2. Finally we fill this into the equation, so we get :y - 7 = -1/2(x - 3)2y + x = 10