Find an equation for the line perpendicular to 2 x + 6 y = 48 and goes through the point ( − 9 , 7 ) . Write your answer in the form y = m x + b

Answer 1

2x + 6y =48

x +3y = 24

3y = -x+24

y =(-1/3)x+ 8 has a slope = -1/3. slope is the coefficient of the x term when a linear equation is solved for y

the perpendicular line has a negative inverse slope. Negative inverse of -1/3 is +3. change the sign and flip the fraction upside down. convert -1/3 to +3/1 = 3

y = 3x + b is the perpendicular line. To find b, plug in the point (-9,7)

7= 3(-9) +b

b =7 +27 = 34

y = 3x +34 is the perpendicular line through the point (-9,7), written in slope intercept form, slope=3, y intercept = 34