Write an equation of the line passing through left parenthesis 9 comma 4 right parenthesis and perpendicular to x plus 3 y equals 24.

Question

Write an equation of the line passing through

left parenthesis 9 comma 4 right parenthesis(9,4)

and perpendicular to

x plus 3 y equals 24x+3y=24.

Answer 1

24x +3y = 24 divide by 3

8x + y = 8

solve for y

y = -8x + 8 has slope = -8 = coefficient of the x term

a perpendicular line has negative inverse slope. change sign and flip the number upside down to get +1/8

y = x/8 + b plug in the point (9,4) to solve for b = y intercept

4 = 9/8 +b

b = 4-9/8 = 4 - 1 1/8 = 2 7/8 = 23/8]

perp line is y = x/8 + 23/8 in slope intercept form

or

8y = x +23

x -8y = -23 in standard form