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