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 Height
(months) (inches)
2 14
4 23
6 32
8 41
To find the equation in slope-intercept form that represents the height of the tree at any time, we need to find the slope and the y-intercept.
First, we need to find the slope. The slope is calculated by taking the difference in height over the difference in time.
Slope = (Change in Height) / (Change in Time)
Slope = (41 - 14) / (8 - 2)
Slope = 27 / 6
Slope = 4.5
Now that we have the slope, we can use the point-slope form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept. We can choose any of the given points to find the y-intercept.
Using the point (2, 14):
14 = 4.5(2) + b
14 = 9 + b
b = 5
Therefore, the equation in slope-intercept form that gives the tree's height at any time is:
Height = 4.5(time) + 5