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?
time (months): 3, 5, 7, 9
plant height (cm): 21, 35, 49, 63
A. y-21=7/2(x-3)
B. y-21=7(x-3)
C. y-3=7/2(x-21)
D. the relationship is nonlinear
Apologies for the mistake. Let's calculate the slope between the first two points (3, 21) and (5, 35) again:
slope = (35 - 21) / (5 - 3) = 14 / 2 = 7
Using the point-slope form equation y - y₁ = m(x - x₁), we can choose the point (3, 21) as our reference point and plug in the slope:
y - 21 = 7(x - 3)
This equation matches option B: y - 21 = 7(x - 3). Therefore, option B is the correct answer. Thank you for pointing out the error.
its B.
To find the equation of the plant's height at any time in point-slope form, we need to calculate the slope between any two points and choose one of the points as the reference.
Let's calculate the slope between the first two points (3, 21) and (5, 35):
slope = (35 - 21) / (5 - 3) = 14 / 2 = 7
Using the point-slope form equation y - y₁ = m(x - x₁), we can choose the point (3, 21) as our reference point and plug in the slope:
y - 21 = 7(x - 3)
This equation matches option A: y - 21 = 7/2(x - 3). Therefore, option A is the correct answer.