Question

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

Answer 1

To find the equation in slope-intercept form that represents the relationship between time and height, we need to find the slope and the y-intercept.

First, we can find the slope using the formula:
slope = (change in height) / (change in time)

Using the data given:
Change in height = 41 - 14 = 27 inches
Change in time = 8 - 2 = 6 months

slope = 27 / 6 = 4.5

Now, we can use the slope-intercept form of an equation:
y = mx + b

Where:
y = height
m = slope
x = time
b = y-intercept

Now, let's plug in the values we know to find the equation:
Using the point (2, 14) on the line:

14 = 4.5 * 2 + b

14 = 9 + b

b = 14 - 9
b = 5

So, the equation in slope-intercept form that gives the tree's height at any time is:
y = 4.5x + 5