Answer: 1.5 inches
Step-by-step explanation:
If two quantities are directly proportional, it means that an increase in the value of one quantity would cause a corresponding increase in the other quantity. Also, a decrease in the value of one quantity would cause a corresponding decrease in the other quantity.
Given that the amount a spring will stretch,S varies directly with weight, F, if we introduce a constant of proportionality, k, the expression becomes
S = kF
When S = 2.22 and L = 37, then
2.22 = 37k
k = 2.22/37 = 0.06
Therefore, the equation that relates the length S that the spring stretches to the weight F is
S = 0.06F
Therefore, if F = 25 pounds, then
S = 0.06 × 25
S = 1.5 inches
8,-4 : 6,-2 : 5,-1 All should add up to four.
To understand problems like these, we must understand how Slope Intercept Form (SIF) works, and how to solve an equation.
<span>A
</span>SIF is "y=mx+b" where "m" is the slope and "b" is the y-intercept.
y='m'x+''b''
y='3'x-''4''
We can see that in this equation, the slope is 3/1 or 3, and the y-intercept is -4.
<u>B
</u>For this one, we must solve for "y," and then proceed with the same thing we did in Part A.
4x-5y=15
-4x -4x
-5y=-4x+15
/-5 /-5
y='4/5'x-"3"
Using the math above, we can see that the slope is 4/5, and the y-intercept is -3.
