Question

jasmine is examining the graph of a scatter plot. when she purchased the plant, it came in a height of 5.5 inches. its height today is 6.5 inches. assuming that the graph also shows average week, which equation models the height of the tomato plant after x weeks of growth? using the graph, estimate the height of the plant in 6 weeks.
options:
a
y = 0.5x + 5.5, about 8.5 inches
b
y = x + 5.5, about 11.5 inches
c
y = 0.5x, about 3.0 inches
d
y = 2x + 5.5, about 17.5 inches
e
y = 0.5x + 2.5, about 5.5 inches

Explanation:

Step1: Identify two points on the line

From the graph, let's assume two clear points. Let's say when \( x = 0 \) (time = 0 months), the height \( y \) (let's check the y - intercept). Also, we know the growth rate. Let's take two points: suppose at \( x = 0 \), \( y = 8 \) (maybe the initial height), and since the growth rate is 0.5 inches per month, the slope \( m = 0.5 \).

The slope - intercept form of a line is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.

Step2: Determine the slope and y - intercept

The slope \( m \) is the rate of change, which is 0.5 inches per month (given that the plant grows 0.5 inches each month). The y - intercept \( b \) is the initial height. From the graph (and the context), when \( x = 0 \) (0 months of growth), let's assume the initial height \( b = 8 \) inches.

So the equation of the line should be \( y=0.5x + 8 \), which can be written as \( y = 8+0.5x \) or \( y=0.5x + 8 \). Let's check the options. Option C is \( y = 0.5x+8 \), which matches our calculation.

Answer:

C. \( y = 0.5x + 8 \), where \( y \) is in inches