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 he…

Question

asked Feb 20, 2019 51.0k views

2 Answers

Shaya · Answer 1 · 2019-02-27T12:27:12+0000

Answer:

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

Explanation:

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

y=mx+b

Where
is the slope
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
.

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:

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