Question

planted, a tree grows at a rate of 0.6 meters per year. After 3 years the tree is 2.2 meters tall. Write the1 in point-slope form that models the situation. Then, predict the height of the tree after 6 years.

Answer 1

`y-2.2=0.6(x-3_{})_{}`

Given that a tree grows at a rate of 0.6 meters per year. After 3 years the tree is 2.2 meters tall.

Let x be the number of years and y be the height of the tree

we get slope m=0.6

And the point is

`(x_1,y_1)=(3,2.2\text{)}`

Recall that the point-slope formula is

`y-y_1=m(x-x_1)_{}`
`\text{ Substitute m=0.6, }x_1=3\text{ and }y_1=2.2,\text{ we get}`

`y-2.2=0.6(x-3_{})_{}`

Substitute x=6 to find the height of the tree after 6 years.

`y-3=0.6(6-2.2_{})_{}`

`y-2.2=0.6(6-3)_{}`
`y-2.2=1.8`

Adding 2.2 on both sides, we get

`y-2.2+2.2=1.8+2.2`
`y=4\text{ meters.}`

Hence the equation in the form of point-slope of the given model is

`y-2.2=0.6(x-3_{})_{}`

The height of the tree of 6 years is 4 meters.

The fourth option is correct.