Question

Weeks after planting a seed, a student measures the plant at 30 cm. After 8 weeks, the plant is 49 cm. Letting x = # of weeks since planting and y = height of the plant in cm, use these two points of data to create a linear model (put your answer in slope-

Answer 1

To create a linear model using the given data points, we need to find the slope and y-intercept of the line that represents the relationship between the number of weeks since planting and the height of the plant.

Step-by-step explanation:

To create a linear model using the given data points, we need to find the equation of the line that represents the relationship between the number of weeks since planting (x) and the height of the plant (y). We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope (m). The slope is calculated by finding the change in y divided by the change in x. Using the two data points (0, 30) and (8, 49), the change in y is 49 - 30 and the change in x is 8 - 0. So, the slope is (49 - 30) / (8 - 0) = 19 / 8.

Next, we need to find the y-intercept (b). We can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). Using the point (0, 30) and the slope we found earlier, the equation becomes y - 30 = (19/8)(x - 0). Simplifying this equation gives us y = (19/8)x + 30.