Question

The line 4x + ky = -1 has a slope of 2/3. Find k.

a. 3/2
b. 6
c. -3
d. -6

Answer 1

To find the slope the equation must be in y=mx+b form

To do this rewrite the equation with y by itself
4x+ky=-1
↓
4x+ky+1=0
↓
4x+1= -ky
↓
(4x+1)/-k=y

Now y is by itself Now separate the equation with -k and the denominator

4x/-k + 1/-k =y is in y=mx+b form

4/-k is m which is your slope

Set 4/-k equal to 2/3 since they give you the slope. Solve for k

4/-k=2/3
↓ Multiply -k on both sides

4=2/3(-k)
↓ Divide by 2/3 on both sides
6= -k
↓ Divide by -1 to remove the - sign from k

-6=k