Question

Line A and Line B are increasing at constant rates. The initial height of Line A is 2 feet. The initial heightof Line B is 3 feet. The height of A after x = 1 (or 1 minute) is 6 feet. The height of B at x = 1 (or 1minute) is 3 1/2 feet.What will be the height in feet of each line at x = 4 (after 4 minutes)? Give a mathematical explanation.

Answer 1

Line A

initial height 2 feet

when x=1

height is 6 ft

y= height

x= minutes

y=mx+b

in our case

b= initial height

then we need to find m

y=6

x=1

b=2

6=m(1)+2

we isolate the m

m=6-2

m=4

The equation that represents line A is

y=4x+2

Then for x=4

y=4(4)+2

y=18

Line A height is 18 ft when x=4

Line B

initial height 3 ft

when x=1 the height of line B is 3 1/2

the form of the equation of line B is

y=mx+b

b is the initial height

y= height

x= minutes

If

x=1

y=3 1/2 ft

3 1/2= m(1)+3

m=1/2

The equation of the line is

y=1/2 x+3

if x=4

y=1/2 (4)+3

y=5

Line B height is 5ft when x=4