Question

a bean plant grows at a constant rate for a month. after 10 days, the plant is 30 centimeters tall. after 20 days, the plant is 50 centimeters tall. which equation models the height of the plant, y, after x days?

Answer 1

Answer:

(y-30)=2(x-10)(y−30)=2(x−10)

Step-by-step explanation:

We have been given that a bean plant grows at a constant rate for a month. after 10 days, the plant is 30 centimeters tall. after 20 days, the plant is 50 centimeters tall.

First of all we will find slope of our line using given points.

m=\frac{y_2-y_1}{x_2-x_1}m=

x

2

−x

1

y

2

−y

1

Upon substituting coordinates of our given points in slope formula we will get,

m=\frac{50-30}{20-10}m=

20−10

50−30

m=\frac{20}{10}=2m=

10

20

=2

Therefore, slope of our given line is 2.

Since the equation of a line in point slope form is (y-y_1)=m(x-x_1)(y−y

1

)=m(x−x

1

) .

Upon substituting m=2 and coordinates of one point in above equation we will get,

(y-30)=2(x-10)(y−30)=2(x−10)

Therefore, the equation that models the height of the plant (y) after x days will be (y-30)=2(x-10)(y−30)=2(x−10) .

Answer 2

Answer:

$(y-30)=2(x-10)$

Step-by-step explanation:        

We have been given that a bean plant grows at a constant rate for a month. after 10 days, the plant is 30 centimeters tall. after 20 days, the plant is 50 centimeters tall.

First of all we will find slope of our line using given points.

$m=\frac{y_2-y_1}{x_2-x_1}$

Upon substituting coordinates of our given points in slope formula we will get,

$m=\frac{50-30}{20-10}$

$m=\frac{20}{10}=2$

Therefore, slope of our given line is 2.    

Since the equation of a line in point slope form is $(y-y_1)=m(x-x_1)$.

Upon substituting m=2 and coordinates of one point in above equation we will get,

$(y-30)=2(x-10)$

Therefore, the equation that models the height of the plant (y) after x days will be $(y-30)=2(x-10)$.