Write the equation of the line that passes through the point (4,-1) and is perpendicular to the line 2x-3y=6. Give the final answer in slope-intercept form.

Answer 1

2x-3y = 6

solve for y

3y= 2x-6

y = 2x/3 -2 is a line with slope = 2/3

a perpendicular line will have the negative inverse of 2/3 which is -3/2. Just change the sign and flip the fraction upside down

y=-3x/2 + b is a perpendicular line. to solve for b plug in the point (4,-1)

-1 = -3(4)/2 + b

b = 5

y=-3x/2 + 5 is the equation of the perpendicular line through the point (4,-1)

y=mx + b is slope intercept form, slope = m=-3/2 and b= intercept = 5

y=(-3/2)x + 5