Question

polly bought a tomato plant from evergreen nursery and planted it in her vegetable garden. she recorded the height of the plant each week after she planted it. this scatter plot shows the data she recorded along with the line of best fit. 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: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the given equation $y = 4x+7$, $m = 4$ and $b = 7$.

Step2: Interpret y - intercept

The y - intercept ($b$) represents the value of $y$ when $x = 0$. In the context of the tomato - plant growth, $x$ is the number of weeks after planting and $y$ is the height of the plant. When $x = 0$ (the time when the plant was planted), $y=4\times0 + 7=7$. So the height of the plant when it was planted was 7 inches.

Step3: Interpret slope

The slope $m = 4$ means that for every 1 - unit increase in $x$ (1 week), $y$ (height) increases by 4 inches. It does not mean 4 inches every 7 weeks.

Answer:

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