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
[tex](x_1,y_1)=(3,2.2\text{)}[/tex]Recall that the point-slope formula is
[tex]y-y_1=m(x-x_1)_{}[/tex][tex]\text{ Substitute m=0.6, }x_1=3\text{ and }y_1=2.2,\text{ we get}[/tex][tex]y-2.2=0.6(x-3_{})_{}[/tex]Substitute x=6 to find the height of the tree after 6 years.
[tex]y-3=0.6(6-2.2_{})_{}[/tex][tex]y-2.2=0.6(6-3)_{}[/tex][tex]y-2.2=1.8[/tex]Adding 2.2 on both sides, we get
[tex]y-2.2+2.2=1.8+2.2[/tex][tex]y=4\text{ meters.}[/tex]Hence the equation in the form of point-slope of the given model is
[tex]y-2.2=0.6(x-3_{})_{}[/tex]The height of the tree of 6 years is 4 meters.
The fourth option is correct.
