The table shows the height of a tree as it grows. What equation in slope-intercept form gives the tree's height at any time?
Time
(months) Height
(inches)
2 14
4 23
6 32
8 41
To find the equation in slope-intercept form that gives the tree's height at any time, we need to find the values of the slope and y-intercept.
First, let's find the slope (m):
m = (change in y) / (change in x)
Here, the change in y is the change in height and the change in x is the change in time.
Change in height = 41 - 14 = 27 inches
Change in time = 8 - 2 = 6 months
m = (27 inches) / (6 months) = 4.5 inches/month
Now, let's find the y-intercept (b).
We can take the values of one of the points given in the table (2, 14) and substitute them into the slope-intercept form equation (y = mx + b) to solve for b.
14 = (4.5 inches/month)(2 months) + b
14 = 9 inches + b
b = 14 - 9 = 5 inches
Therefore, the equation in slope-intercept form that gives the tree's height at any time is:
Height (in inches) = 4.5 (time in months) + 5