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 (months) Plant Height (cm)
2 14
4 28
6 42
8 56
56
(y - 14) = 7 (x - 2)
y=7x
So I wonder which one is right ??
To find the equation in point-slope form that gives the plant's height at any time, we need to use the given data to determine the slope and a point on the line.
First, let's find the slope (m) using the formula:
m = (change in y)/(change in x)
In this case, the change in y represents the change in plant height, and the change in x represents the change in time. Taking any two points from the table, we can calculate the slope:
m = (28 - 14)/(4 - 2) = 14/2 = 7
The slope of 7 indicates that for every 1 month increase in time, the plant's height increases by 7 cm.
Next, we can choose any point from the table to substitute into the point-slope form equation. Let's use the point (2, 14):
The equation in point-slope form is given by:
y - y1 = m(x - x1)
where (x1, y1) is the point and m is the slope.
Substituting the values, we get:
y - 14 = 7(x - 2)
Simplifying further:
y - 14 = 7x - 14
OR
y = 7x
Therefore, the equation in point-slope form that gives the plant's height at any time is y = 7x.