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
2 14 difference column below
******** 14
4 28
******** 14
6 42
******** 14
8 56
oh my, whenever the month changes by 2, the height changes by 14
so the slope is m = 14 cm/ 2 months = 7 cm/month
so
h = 7 t + b
what is b?
well the first point is at 2 months, and the height is amazingly 14
so I claim it started at 0 height when t was zero (tiny seed)
so
h = 7 t
the end
To find the equation in point-slope form that relates the time (months) to the plant's height, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where y is the dependent variable (plant height), x is the independent variable (time in months), m is the slope, and b is the y-intercept.
To determine the slope, we'll use the formula:
m = (change in y) / (change in x)
We can choose two points from the table to calculate the slope. Let's choose (2, 14) and (4, 28):
m = (28 - 14) / (4 - 2)
m = 14 / 2
m = 7
Now we have the slope (m = 7). To find the y-intercept (b), we can choose any point from the table. Let's choose (2, 14):
14 = 7(2) + b
14 = 14 + b
b = 0
The equation in point-slope form is:
y = 7x + 0
Simplified, this equation becomes:
y = 7x
To find the equation in point-slope form for the plant's height at any time, we need to first identify the slope of the line. The slope of a line can be determined by finding the change in y (plant height) divided by the change in x (time).
Let's take the first two points (2, 14) and (4, 28) to find the slope:
slope = (change in y) / (change in x)
= (28 - 14) / (4 - 2)
= 14 / 2
= 7
Now we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Let's use the point (2, 14):
y - 14 = 7(x - 2)
Expanding the equation:
y - 14 = 7x - 14
Simplifying the equation:
y = 7x
Therefore, the equation in point-slope form that gives the plant's height at any time is y = 7x.