10. The table shows the height of a plant as it grows.

Question

What equation in point-slope form gives the plant’s height

time (months) | plant height (cm)
2 | 14
4 | 28
6 | 42
8 | 56

and simplify answer if possible

Answer 1

To find the equation in point-slope form, we can choose any two points from the table and use the point-slope formula:

(y - y1) = m(x - x1)

Let's choose points (2, 14) and (4, 28):

Using the formula, we have:

(plant height - 14) = m(time - 2)

Substituting the values of the second point, we get:

(28 - 14) = m(4 - 2)

14 = 2m

Dividing both sides by 2:

m = 7

Now we can use one of the points along with the slope we just found (m = 7) to write the equation in point-slope form.

Let's use the first point (2, 14):

(y - 14) = 7(x - 2)

Simplifying if possible:

y - 14 = 7x - 14

y = 7x

Thus, the equation in point-slope form that represents the plant's height is y = 7x.