Question

The amount a string stretches varies linearly with the mass applied to the spring, as can be seen in the video. In the video, with no additional mass, the hanger was 30.6 cm off the ground. With 150 grams of additional mass, the hanger was 16.2 cm off the ground.

A wooden block stretched the spring so the hanger was 21.2 cm off the ground. Determine the mass of the wooden block, to at least 1 decimal place.

Answer 1

Based on the description of the question, we can say that the stretch is dependent on the mass applied, and it's given that there is a linear relationship. Hence, you can designate x=mass in g and y= height in cm off the ground.

Then, the given points would be (0, 30.6) and (150, 16.2). Using these points, you must find the relation representing it in y=mx+b. You already are given b which is the initial value when mass = 0g. Now use those points to find the slope, m.

After that, you are asked to find the mass of the wooden block when given the height off the ground, 21.2 cm. You would plug this in as y, and solve for x. That is the mass. Remember to round to at least 1 decimal place.

Answer 2

So it seems like you have trouble setting it up.
First make the equation using the given values, (0, 30.6) and (150, 16.2) in terms of (grams, height). For that, you need the slope and the y-intercept. Now, to our convenience, the y-intercept is already given. It's when mass is 0. Hence, b=30.6.
\(y=mx+30.6\)
Now to find m, use the slope formula
\(m=\frac{y_2-y_1}{x_2-x_1}\), and use the points (0, 30.6) and (150, 16.2). You'll get m=-0.096. Thus, our equation looks like this:
\(y=-0.096x+30.6\)
It's asking for the specific mass of the wooden block when the height off the ground was 21.2 cm. Set y=21.2 and solve for x
\(21.2=-0.096x+30.6\)
I'm sure you can find x now.