If the points (2, 4), (5, k), and (8, 20) are on the same line, what is the value of k?

k = 12

Step-by-step explanation:

Calculate the slope m using the slope formula

m =

with (x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (8, 20)

m = = =

Repeat using (5, k) as one of the points and equate to

(x₁, y₁ ) = (2, 4) and (x₂, y₂ ) = (5, k) , then

m = = = ( cross- multiply )

3(k - 4) = 24 ( divide both sides by 3 )

k - 4 = 8 ( add 4 to both sides )

k = 12

the answer would be  

a.

3: 1

step-by-step explanation:

d: (13,-1)

step-by-step explanation:

we know the starting point is (1,5)

the ending point is (x,y)   (cristians house)

the total distance is 6 units (5: 1)  

the fast food restaurant is at (11,0) and is 5/6ths of the way from the starting point to the ending point

ending minus starting point * 5/6   is how far they went

(x-1) *5/6, (y-5) * 5/6

we then need to add the starting point to determine the location

5/6(x-1) + 1, (y-5) * 5/6 + 5

this equals the fast food location of 11,0

setting the x locations equal

5/6 (x-1) +1 =11

subtracting 1 from each side

5/6 (x-1) +1-1 =11-1

5/6(x-1) =10

multiplying by 6/5 on each side

6/5*5/6(x-1) = 10*6/5

x-1 =12

add 1 to each side

x-1+1 =12+1

x=13

do the same for the y coordinate

(y-5) * 5/6 + 5 =0

subtract 5 from each side

(y-5) * 5/6 + 5-5 =0-5

5/6 (y-5) = -5

multiplying by 6/5 on each side

6/5*5/6 (y-5) = -5 *6/5

y-5 = -6

add 5 to each side

y-5+5 = -6+5

y=-1

the ending point , or the coordinates of cristians house is

(13,-1)