Question

jack is doing an experiment to find the rate of water flow from a tap. he collects the water in a tub and records the height of the water - level every five minutes. he then plots the data on a scatter plot. which equation represents the line of best fit for jacks scatter plot? a. (y = \frac{14}{45}x) b. (y = 45x+14) c. (y = \frac{45}{14}x) d. (y = 14x + 45)

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.

Step2: Estimate y - intercept

The line of best fit appears to cross the y - axis at approximately $y = 5$.

Step3: Calculate slope

We can use two points on the line. Let's take $(0,5)$ and $(14,45)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{45 - 5}{14-0}=\frac{40}{14}=\frac{20}{7}\approx\frac{40}{14}$.

Step4: Check equations

For option A, $y=\frac{40}{14}x$, when $x = 0$, $y = 0$. But our y - intercept is around 5, so A is incorrect.
For option B, $y = 45x+14$, the slope is 45 which is much steeper than our line, so B is incorrect.
For option C, $y=\frac{40}{14}x$, we can rewrite it as $y=\frac{20}{7}x$. This has the correct - approximate slope and we can assume the y - intercept is close enough to 0 for a line of best fit approximation in this case.
For option D, $y = 14x+45$, the slope is 14 which is steeper than our line and the y - intercept is 45 which is too high, so D is incorrect.

Answer:

C. $y=\frac{40}{14}x$