The table shows the height of a plant as it grows. Which equation in point-slope form form gives the plants height at any time?
Time | Plant Height
3 | 21
5 | 35
7 | 49
9 | 63
A) y-21=7/2 (x-3)
B) y-21=7 (x-3)
C) y-3=7/2 (x-21)
D) This relationship is non-linear
To determine the correct equation in point-slope form that gives the plant's height at any time, we need to find the slope between two points (time and height) on the table.
Using the points (3, 21) and (5, 35), we can find the slope:
slope = (change in height) / (change in time)
= (35 - 21) / (5 - 3)
= 14 / 2
= 7
Therefore, the slope of the line representing the plant's height is 7.
Now, we need to use the point-slope form of an equation:
y - y1 = m(x - x1)
where (x1, y1) is any point on the line and m is the slope.
Using the point (3, 21) as our reference point, we have:
y - 21 = 7(x - 3)
This equation simplifies to:
y - 21 = 7x - 21
So, the correct equation in point-slope form that gives the plant's height at any time is:
y - 21 = 7(x - 3)
Therefore, the answer is A) y - 21 = 7/2 (x - 3).