I need help proving my answer. Will medal: Ravi hangs from a giant exercise spring whose length is 5m. When his child Nimi hangs from the spring, its length is 2m. Ravi weighs 160lbs and imi weighs 40lbs. Write the equation for this problem in slope-intercept form. What should we expect the length of the spring to be when his wife Amardeep, who weighs 140lbs, hangs from it?

Question

anonymous · Answer

Values gathered: (5, 160); (2, 40); (x, 140)
Solving for Slope: $$\frac{ y_2 - y_1 }{ x_2 - x_1 } = \frac{ 40 - 160 }{ 2 - 5 } = \frac{ -120 }{ -3 } = (-40)$$

anonymous · Answer

Solving for y-intercept:
$$y = mx + b$$$$160 = -40(5) + b$$$$160 = -200 + b$$$$360 = b$$

anonymous · Answer

Solving for Amardeep's x, (x, 140):
$$y = -40x + 360$$$$140 = -40x + 360$$$$-220 = -40x$$$$\frac{ -220 }{ -40 } = \frac{ 11 }{ 2 } = x$$

anonymous · Answer

I saw a sign mistake. slope = 40. So doing the math again, I got x = 9/2.

anonymous · Answer

Yep, slope is 40, and the final answer is 9/2 or 4.5 ft.
The way you did it was weird though, here's how I'd do it if you're interested.


You'd have to use point-slope form to plug in an x AND a y to find y-intercept.
So point slop form is y-y1=m(x-x1)
So you'd have y-160=40(x-5)
Which simplifies to y=40x-200+160
y=40x-40
^that's your formula.
Now to find the spring's length (x) when Amardeep weighs 140 (y),
y=mx+b
140=40x-40
40x=180
x=9/2