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)
2
4
6
8
Height
(inches)
14
23
32
41
To find the equation in slope-intercept form, we need to determine the slope and the y-intercept.
First, let's find the slope. The formula for slope is given by:
m = (y2 - y1) / (x2 - x1)
Using the points (2, 14) and (8, 41) from the table, we plug in the values into the slope formula:
m = (41 - 14) / (8 - 2)
m = 27 / 6
m = 4.5
Now, let's find the y-intercept. The y-intercept is the value of y when x = 0. From the table, we can see that when time (months) is 0, the height (inches) is unknown. Therefore, we do not have enough information to determine the y-intercept.
However, we can write the equation in point-slope form using the information we have and the slope we calculated.
Using the point (2, 14), we can write:
y - y1 = m(x - x1)
y - 14 = 4.5(x - 2)
Simplifying and rewriting the equation in slope-intercept form:
y - 14 = 4.5x - 9
y = 4.5x + 5
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.