Question

the equation for the line of best fit is y = 4x + 7. according to the equation, which of these statements is true? the tomato plant was about 7 inches tall when polly planted it. the tomato plant grew about 4 inches every 7 weeks.

Explanation:

Step1: Analyze the linear equation form

The equation of the line is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=4x + 7\), the slope \(m = 4\) and the y - intercept \(b = 7\).

Step2: Interpret the y - intercept

The y - intercept (\(b\)) occurs when \(x = 0\). In the context of the tomato plant's growth, \(x\) represents the number of weeks since the plant was planted, and \(y\) represents the height of the plant. When \(x = 0\) (at the time of planting), \(y=4(0)+7=7\). This means that the height of the tomato plant at the time of planting (when Polly planted it) was 7 inches.

Step3: Analyze the slope interpretation (for the other statement)

The slope \(m = 4\) means that for every 1 - unit increase in \(x\) (every 1 week), the height \(y\) (in inches) increases by 4. So the statement "The tomato plant grew about 4 inches every 7 weeks" is incorrect because the slope of 4 implies 4 inches growth per 1 week, not per 7 weeks.

Answer:

The tomato plant was about 7 inches tall when Polly planted it.