Solve Equation of Line with Slope of 1¼

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To solve an equation of a line with a slope of 1¼, convert the mixed number into an improper fraction, resulting in 5/4. The formula used is y - y1 = m(x - x1), where m represents the slope. The conversion process involves multiplying the whole number by the denominator and adding the numerator. An alternative method is to express the mixed number as a sum of its whole and fractional parts. Understanding this conversion is essential for applying the slope in line equations.
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Homework Statement


i just want to know how i go about it when the slope contains a whole number and a fraction, i.e. 1¼

Homework Equations


y - y1 = m(x - x1)


The Attempt at a Solution

 
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Change the number into an improper fraction. Do you know how to do that?

For instance,
2\frac{1}{3} = \frac{7}{3}
 
i didn't no, but from the looks of it you multiply the whole number by the denominator and add the numerator

so i got it, much appreciated
 
tehmatriks said:
i didn't no, but from the looks of it you multiply the whole number by the denominator and add the numerator

so i got it, much appreciated

Another way to think of it:

"Two and one-third" = 2+\frac{1}{3} ("and" typically means addition)

Think of a fraction with a denominator of 3 that is also equal to 2.

\frac{6}{3}+\frac{1}{3}=\frac{7}{3}

This is probably a bit more work than what's necessary, but I find it much more interesting. :biggrin:
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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