find the equation of the line in all 3 forms- point slope, slope intercept and standard

Question

perpendicular to -4x - 7y = 6, through (-4, 7)

Answer 1

-4x -7y = 6

4x + 7y = -6

7y = -4x -6

y = (-4/7)x - 6/7 is in slope intercept form with -4/7 = slope and -6/7 = y intercept but

the perpendicular line has slope = the negative inverse. change the sign and flip the fraction upside down to go from -4/7 to +7/4

y = (7/4)x + b to solve for b plug in the point (-4,7) x=-4, y =7

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

b =14

y = (7/4)x + 14 is in standard slope intercept form for the perpendicular line through (-4,7)

general slope intercept form is y=mx +b where m= slope and b = intercept

in point slope form

(y-7)/(x - -4) = 7/4

or y-7 = (7/4)(x+4)

general point slope form is (y-y1)/(x-x1) = m or (y-y1)=m(x-x1) where m=slope and (x1,y1) is the point

general standard form for a linear equation is Ax+By+C = 0

4x + 7y + 6 = where A=4, B=7 and C = 6