MHB Word Problem for slope intercept graph equation

AI Thread Summary
The discussion revolves around solving a word problem related to a shipping cost function based on weight. The key points include identifying the ordered pairs (4, 3.55) and (6, 4.35) to determine the slope, which is calculated as 0.4. Participants explain how to use the point-slope form of a linear equation to derive the cost function, emphasizing that the equation can be expressed as c = aw + b. The process involves setting up two equations based on the given points and solving for the coefficients a and b. The conversation highlights the steps necessary to create the equation for the shipping cost based on weight.
mhester88
Messages
3
Reaction score
0
I have this word problem that is asking for two different answers, the equation for the data and to calculate the shipping rate. I'm not understanding how to address either of the questions. Will someone please help me with this answer?

IMG-6771.jpg
 
Mathematics news on Phys.org
shipping cost is dependent on weight

an ordered pair for the cost function would be $(w, c)$ where $w$ is the weight (the independent variable), and $c$ is the cost (the dependent variable

you are given two such ordered pairs, $(4, 3.55)$ and $(6, 4.35)$

find the slope between those two given points, then use the point-slope form of a linear equation to get the cost function
 
Thank you for your response. If I'm understanding this correctly, then the slope would be 0.4. I'm still confused on how to write the equation using c and w. I'm not sure how to even begin creating the equation.
 
mhester88 said:
Thank you for your response. If I'm understanding this correctly, then the slope would be 0.4. I'm still confused on how to write the equation using c and w. I'm not sure how to even begin creating the equation.

point-slope form of a linear equation ...

$y - y_1 = m(x - x_1)$

where $(x_1,y_1)$ is a point on the line and $m$ is the slope

... requires one point (you have two), and the slope, $m$.

remember, y is the cost (you can use c instead) and x is the weight (you can use w instead)

$c - c_1 = m(w - w_1)$
 
Any (non-vertical) line has equation c= aw+ b for some numbers, a and b. You are told that when the weight, w, is 4 lb. the cost, c, is \$3.55 so 3.55= a(4)+ b. You are told that when the weight, w, is 6 lb. the cost, c, is \$4.35 so 4.35= a(6)+ b.

Solve the two equations, 4a+ b= 3.55 and 6a+ b= 4.35, for a and b. I recommend you subtract the first equation from the second to eliminate b.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Thread 'Imaginary Pythagorus'
I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...
Back
Top