Question

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

Answer 1

(3,21)(5,35)
slope = (35 - 21) / (5 - 3) = 14/2 = 7

possible answers are :
y - 21 = 7(x - 3)
or
y - 35 = 7(x - 5)
or
y - 49 = 7(x - 7)
or
y - 63 = 7(x - 9)

Answer 2

y - 21 = 7(x - 3)

Explanation:

If we plot the points on a graph having time on x axis and plant height on y axis then the two points will be (3, 21) and (5, 35).

Let the equation of the line is y - y'= m(x - x')

where m = slope of the line

Now slope of the line joining these points 'm' =
`(y-y')/(x-x')`

m =
`(35-21)/(5-3)`

m =
`(14)/(2)`

m = 7

Now the equation that passes through the point (3, 21) will be y - 21 = 7(x - 3)

Therefore, equation that represents the height of the plant at any time is y - 21 = 7(x - 3)