Math problem solve

Question

Using the company's most popular brand of rope material, your team determined a rule for a standard length of rope and the number of knots as:

L(k)=200−12k

where kk is the number of knots in the rope and L(k) is the length of rope having k knots.

What would be the slope

Whats the length lost per knot

Answer 1

slope is the coefficient of the linear term, when the equation is solved for the dependent variable

L(k) is the dependent variable, dependent on k

-12 is the coefficient of the independent linear term, k.

slope =-12

Answer 2

The formula given can be rewritten in standard form of y = mx+b

where m is the slope

and b is the y intercept

rewriting the given equation, we can substitute

L(k) = y

k = x

-12 = m

200 = b

which means that the slope (m) is -12

The length lost per knot is 12. If there were 0 knots the length would be 200. If you add one knot the length would be 188. The difference for adding 1 knot is 12.

Answer 3

Hi Justin!

Recall that slope-intercept form of a line can be express as y = mx + b where m is the slope, x is the x coordinate, and b is the y-intercept. In this problem we are just substituting k for x.

So, the slope is the value in front of k. The slope is -12.

The length lost per knot would also be 12 by definition of slope. You can also plug numbers into the rope length equation to prove this. Let's try 7 and 8 knots.

L(8) = 200 -12(8) = 104

L(7) = 200 - 12(7) = 116

When you go from 7 knots to 8 knots, the length decreases by 12 units. Hope that helps you!

Answer 4

L(k) = -12k + 200, slope is -12

The rope loses 12 (units not specified) per knot.

Answer 5

Looks like the length of rope is 200 (ft, in, meters?) because that's L(k) when k = 0 (no knots).

The slope is -12, so apparently the rope shortens by 12 units for every knot.