The table shows the height of a plant as it grows. Which equation in point-slope form gives the plant's height at any time?

Question

Time (months)
3
5
7
9
Plant height (cm)
21
35
49
63

Answer 1

Let's use the formula for point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.

By observing the data, we can determine the slope to be 14 (since the rise in height is 14 cm for each interval of 2 months).

Let's choose the point (3, 21) as a reference point.

Using the point-slope form equation, we have:

y - 21 = 14(x - 3)

Simplifying the equation:

y - 21 = 14x - 42

y = 14x - 42 + 21

y = 14x - 21

Therefore, the equation in point-slope form that gives the plant's height at any time is y = 14x - 21.