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) Plant Height (cm)
3 21
5 35
7 49
9 63
To find the equation in point-slope form, we need to determine the slope (change in height over change in time) and the y-intercept (height when time is 0).
First, let's find the slope:
The change in height from 3 months to 5 months is 35 - 21 = 14 cm.
Therefore, the change in time is 5 - 3 = 2 months.
The slope is the change in height divided by the change in time: slope = 14 / 2 = 7 cm/month.
Next, let's find the y-intercept.
At 3 months, the height is 21 cm.
So, the y-intercept is 21.
Therefore, the equation in point-slope form is:
y - 21 = 7(x - 3)