Question

a spring stretches linearly as weight is added. the table shows data collected for a certain spring.

weight in lb (x)	stretch in cm (y)
500	2.5
800	4.0
900	4.5
1,200	6.0

what is the slope of the line that fits these data?

• $\frac{1}{50}$
• $\frac{1}{100}$
• $\frac{1}{200}$
• $\frac{1}{2}$

Explanation:

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step2: Pick two data points

Use $(x_1,y_1)=(100, 0.5)$ and $(x_2,y_2)=(500, 2.5)$

Step3: Calculate slope

$m = \frac{2.5 - 0.5}{500 - 100} = \frac{2}{400} = \frac{1}{200}$

Step4: Verify with other points

Use $(800,4.0)$ and $(1200,6.0)$: $m = \frac{6.0 - 4.0}{1200 - 800} = \frac{2}{400} = \frac{1}{200}$

Answer:

$\frac{1}{200}$