General Form of Equation of A Line

[nycmathguy]

See attachment for question. I need help questions 82 and 86.

 

[MathLover1]

81.

x/a+y/b=1

x-intercept: (a,0)=(3,0)
y-intercept: (0,b)=(0,5)

x/3+y/5=1

(x/3)*15+(y/5)15=1*15

5x+3y=15


82.

x-intercept: (a,0)=(-3,0)
y-intercept: (0,b)=(0,4)

x/-3+y/4=1

(-x/3)*12+(y/4)12=1*12

-4x+3y=12

83.

x-intercept: (a,0)=(-1/6,0)
y-intercept: (0,b)=(0,-2/3)

x/(-1/6)+y/(-2/3)=1
6x/(-1)+3y/(-2)=1 ......multiply by 2
-12x+3y=2

84.

x-intercept: (a,0)=(2/2,0)
y-intercept: (0,b)=(0,-2)

x/(2/3)+y/(-2)=1
3x/2+y/(-2)=1 ......multiply by 2
3x-y=2


85.
point on line: (1,2)
x-intercept: (c,0) =>a=c
y-intercept: (0,c)=> b=c

x/a+y/b=1......substitute a and b

x/c+y/c=1..........use given point (1,2), substitute x and y

1/c+2/c=1.........solve for c

3/c=1
3=c

x-intercept: (3,0)
y-intercept: (0,3)

equation is

x/3+y/3=1.....multiply by 3
x+y=3


86.

point on line: (-3,4)
x-intercept: (d,0) =>a=d
y-intercept: (0,d)=> b=d

x/a+y/b=1......substitute a and b
x/d+y/d=1....multiply by d
x+y=d........use given point (-3,4), substitute x and y
-3+4=d
d=1

x/1+y/1=1
x+y=1

 

[MathLover1]

81.

x/a+y/b=1

x-intercept: (a,0)=(3,0)
y-intercept: (0,b)=(0,5)

x/3+y/5=1

(x/3)*15+(y/5)15=1*15

5x+3y=15


82.

x-intercept: (a,0)=(-3,0)
y-intercept: (0,b)=(0,4)

x/-3+y/4=1

(-x/3)*12+(y/4)12=1*12

-4x+3y=12

83.

x-intercept: (a,0)=(-1/6,0)
y-intercept: (0,b)=(0,-2/3)

x/(-1/6)+y/(-2/3)=1
6x/(-1)+3y/(-2)=1 ......multiply by 2
-12x+3y=2

84.

x-intercept: (a,0)=(2/2,0)
y-intercept: (0,b)=(0,-2)

x/(2/3)+y/(-2)=1
3x/2+y/(-2)=1 ......multiply by 2
3x-y=2


85.
point on line: (1,2)
x-intercept: (c,0) =>a=c
y-intercept: (0,c)=> b=c

x/a+y/b=1......substitute a and b

x/c+y/c=1..........use given point (1,2), substitute x and y

1/c+2/c=1.........solve for c

3/c=1
3=c

x-intercept: (3,0)
y-intercept: (0,3)

equation is

x/3+y/3=1.....multiply by 3
x+y=3


86.

point on line: (-3,4)
x-intercept: (d,0) =>a=d
y-intercept: (0,d)=> b=d

x/a+y/b=1......substitute a and b
x/d+y/d=1....multiply by d
x+y=d........use given point (-3,4), substitute x and y
-3+4=d
d=1

x/1+y/1=1
x+y=1

 

[nycmathguy]

Thank you but I only needed 82 and 86 as a guide for me to do the rest.