Question

The equation for line g is given by 5y=2x-20. Suppose line g is parallel to like r and line e is perpendicular to line g. Point (10,-8) lies on both line r and line E. write an equation for line E

Answer 1

5x + 2y = 34

Explanation:

The desired line is perpendicular to 5y = 2x -20 and goes trhough point (10, -8).

General Approach

You can write the equation of a perpendicular line through (h, k) by ...

• dropping any added constant from the given line's equation
• swapping the x- and y-coefficients, and negating one of them
• replacing x with (x-h) and y with (y-k)

Then, you can put the equation in the form you desire.

This Problem

... 2(y+8) = -5(x-10) . . . . . coefficients swapped, negated; replacements made

... 2y + 16 = -5x +50 . . . . eliminate parentheses

... 5x +2y + 16 = 50 . . . . .add 5x

... 5x + 2y = 34 . . . . . . . . subtract 16. This the equation in standard form.