The table shows the height of a plant as it grows.
What equation in point-slope form gives the plant's height at any time?
Time
Plant Height
(months)
(cm)
2
14
4
28
6
42
8
56
To find the equation in point-slope form that represents the plant's height at any time, we can use the given data points (2, 14), (4, 28), (6, 42), and (8, 56).
Let's choose the point (2, 14) as the initial point for our equation. We can start by finding the slope between the initial point and any other point on the graph.
The slope can be calculated using the formula: slope = change in y / change in x.
Let's choose the point (4, 28) to calculate the slope:
change in y = 28 - 14 = 14
change in x = 4 - 2 = 2
slope = 14 / 2 = 7
Now, using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope (m = 7) and one of the points (x = 2, y = 14) into the equation to find the y-intercept.
14 = 7(2) + b
14 = 14 + b
b = 0
So, the equation of the plant's height at any time in point-slope form is:
y - 14 = 7(x - 2)