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
Is it B? B) y-21=7 (x-3)
Billy Bob
To find the equation of the plant's height at any time, we can use the point-slope form of a linear equation. The point-slope form is given by y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
Now, we can find the slope using two points from the table. Let's take the points (3, 21) and (5, 35):
m = (y₂ - y₁) / (x₂ - x₁)
= (35 - 21) / (5 - 3)
= 14 / 2
= 7
We have the slope, which is 7. Let's choose the point (3, 21) as our reference point.
Now we can substitute the slope and the reference point into the point-slope form to get the equation.
y - y₁ = m(x - x₁)
y - 21 = 7(x - 3)
Thus, the correct equation in point-slope form is:
A) y - 21 = 7/2 (x - 3)
Answer: A) y - 21 = 7/2 (x - 3).
sure looks to me like y=7x
so, which choice would that be?