Final Answer:
The equation of the line that models the growth of the plant can be written in point-slope form as:
y - 2 = m(x - 5)
where y is the height of the plant (in inches) at any given week x, and m is the slope of the line (which represents the rate of growth).
To find the slope m, we can use the fact that the plant was 2 inches tall at week 5, so the point (5, 2) is on the line. Using the slope formula, we have:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. In this case, (x1, y1) = (5, 2) and (x2, y2) = (10, 8), so:
m = (8 - 2) / (10 - 5) = 6 / 5 = 1.2
Now we can write the equation of the line in slope-intercept form as:
y = 1.2x + 2
Step-by-step explanation:
To find the equation of the line that models the growth of the plant, we need to find the slope of the line and the y-intercept. The slope tells us the rate of growth, and the y-intercept tells us the starting height of the plant.
First, we can find the slope of the line by using the fact that the plant was 2 inches tall at week 5. Let’s call the height of the plant at week 5 “h”. Then we can write:
h = 2
Next, we can find the height of the plant at week 10 by using the fact that the plant grew by 6 inches over the 10 weeks:
h10 = h + 6
Substituting h = 2, we get:
h10 = 2 + 6 = 8
Now we can find the slope of the line by using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. In this case, (x1, y1) = (5, 2) and (x2, y2) = (10, 8), so:
m = (8 - 2) / (10 - 5) = 6 / 5 = 1.2
Finally, we can write the equation of the line in point-slope form as:
y - 2 = m(x - 5)
or in slope-intercept form as:
y = 1.2x + 2