Question

Find the equation of the straight line passing through the point (3,5) which is the perpendicular to the line

Y=3x+2

Answer 1

x + 3y = 18 is the equation in standard form.

In slope-intercept form it is y = -1/3 x + 6.

Explanation:

The given line y = 3x + 2 has a slope of 3 so the line perpendicular to it has slope -1/3.

y - y1 = m(x - x1) where m = slope and (x1, y1) is a point on the line.

Using the point (3, 5) our equation is:

y - 5 = -1/3(x - 3) Multiply through by -3:

-3y + 15 = x - 3

x + 3y = 15 + 3

x + 3y = 18 is the required equation.