Question

Ximena bought a plant and planted it in a pot near a window in her house. Let H represent the height of the plant, in inches, t months since Ximena bought the plant. The table below has select values showing the linear relationship between t and H. Determine how many months it would take for the plant's height to reach 63 inches.

Answer 1

Unfortunately, I cannot see the table you are referring to. However, if we assume that the relationship between the height of the plant and time is linear, we can use the slope-intercept form of a linear equation, which is:

y = mx + b

where y is the dependent variable (in this case, the height of the plant), x is the independent variable (time), m is the slope of the line, and b is the y-intercept (the value of y when x is 0).

If we have two points on the line (t1, H1) and (t2, H2), we can find the slope of the line using the formula:

m = (H2 - H1) / (t2 - t1)

Once we have the slope, we can use the point-slope form of a line to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is one of the points on the line. We can then rearrange this equation to the slope-intercept form to find the value of b:

y = mx + b

Once we have the equation of the line, we can plug in the value of y (63 inches) and solve for x (the number of months) to find how long it would take for the plant to reach a height of 63 inches.

For example, if we have two points on the line, (2, 20) and (6, 50), the slope of the line is:

m = (50 - 20) / (6 - 2) = 30/4 = 7.5

Using the point-slope form of the line with the point (2, 20), we get:

y - 20 = 7.5(x - 2)

Simplifying this equation, we get:

y = 7.5x + 5

To find how long it would take for the plant to reach a height of 63 inches, we can plug in y = 63 and solve for x:

63 = 7.5x + 5

58 = 7.5x

x = 7.73

So it would take approximately 7.73 months for the plant to reach a height of 63 inches, assuming that the relationship between the height of the plant and time is linear.