Linear Law (straight-line Form)
Bayani Gaba-gaba
Experimental data rarely falls on a straight line, but a clever change of variables can often make it do so. By taking logarithms, a power law or an exponential law can be straightened into the form \(Y=mX+c\). Then the gradient and intercept of the straight-line graph hand you the unknown constants.
In this lesson you will convert relationships such as \(y=Ax^n\) and \(y=Ab^x\) into straight-line form by taking logarithms, identify what to plot, and read off the constants from the gradient and intercept. This is the bridge between curved real-world data and the simple line you know how to analyse.
Manufura
- Transform given relationships, such as y = Ax to the power n and y = Ab to the power x, to and from straight-line form.
- Determine unknown constants by calculating the gradient or intercept of the transformed straight-line graph.
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Barka da kammala darasi akan Linear Law (straight-line Form). Yanzu da kuka bincika mahimman ra'ayoyi da ra'ayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- To straighten y = Ax^n, you plot: A. y against x B. lg y against lg x C. lg y against x D. y against lg x Answer: B
- To straighten y = Ab^x, you plot: A. lg y against lg x B. lg y against x C. y against x D. y against lg x Answer: B
- Taking logs of y = Ax^n gives: A. lg y = n lg x + lg A B. lg y = A lg x + n C. lg y = lg x + n lg A D. y = n lg x + A Answer: A
- If lg y against lg x has gradient 3 and intercept 0.7 for y = Ax^n, then n is: A. 0.7 B. 3 C. 10^0.7 D. 0.3 Answer: B
- If the intercept of the straight-line graph is lg A = 1, then A equals: A. 1 B. 10 C. 0.1 D. 100 Answer: B
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