Answer:
1) The equation in point and slope form is y - 56 = 3·(x - 17)
2) The above equation in slope and intercept form is y = 3·x + 5
3) The height of the sidling when the botanist received it = 5 inches
4) The height of the tree on week 30 = 7 feet 11 inches
Step-by-step explanation:
The given parameters for the equation are;
The rate of growth of the young tree = 3 inches/week
The current height of the tree = 4 feet 8 inches = 56 inches
The current time since start of growth (time duration of growth) = 17 weeks
With the given information, we have;
The height of the tree, y = The dependent or y-variable
The time for the growth, x = The independent or x-variable
The slope = the rate of growth = 3 inches/week
At week, x = 17, y = 56 inches
1) The information presented in point and slope form is given as follows;
y - 56 = 3·(x - 17)
2) Simplifying the above equation to slope and intercept form, y = mx + c
Where;
m = The slope
c = The y-intercept
We have;
y = 3·x - 51 + 56 = 3·x + 5
y = 3·x + 5
Therefore the y-intercept = 5
3) The y-intercept = 5 which gives the value of the height of the tree at time x = 0 as follows;
At x = 0 when the tree was first received, the height of the tree, y = 3·x + 5 = 5 inches
4) On week 30, the height, y of the tree will be, y = 3 × 30 + 5 = 95 inches = 7 feet 11 inches.
