Algebra, Equation of Linear Functions

Question

How do I write an equation of the line that passes through (-3,4), and perpendicular to -2x+7y=-3

Answer 1

solve for y

7y=2x-3

y = (2/7)x - 3/7

take the negative inverse of the x coefficient, change its sign and flip it upside down to get -7/2

y =-(-7/2)x + b is the equation of a perpendicular line with y intercept b. to calculate b, plug in the point where x =-3 and y=4

4 = (-7/2)(-3) + b

b = 4- 21/2 = -13/2

y= (-7/2)x -13/2

IF you want eliminate the fractions by multiply by 2

2y =-7x -13 or

7x + 2y =-13