Question

A bean plant grows at a constant rate for a month. After 10 days, the plant is 25 centimeters tall. After 20 days, the plant is 45 centimeters tall.

Which equation models the height of the plant, y after x days?

Answer 1

y-25=2(x-10)

Explanation:

Answer 2

B.
`y-25=2(x-10)`

Explanation:

The equation that will model the height
`y` of the plant after
`x` days will be of the form:

`y=mx+b`

Where
`m` is the slope
`b` is the y-intercept.

The slope of the line is:

`m=(45cm-25cm)/(20days-10days) =2\:(cm/day).`

Therefore we have

`y=2x+b`

All we need now is the value of
`b`.

We know that after 10 days the plant is 25 centimeters tall, or at
`x=10`
`y=25`; thus

`25=2(10)+b`

`\therefore b=5`

so we have the equation:

`\boxed{y=2x+5}`

Of the four choices, choice B matches our result, because when we rearrange it and solve for y we get:

`y-25=2(x-10)\\y=2(x-10)+25\\y=2x-20+25\\ \boxed{y=2x+5}`