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3 years ago

Write a equation in standard form that contains a slope of 3 and contains (1,6)

Mathematics

1 answer:

jeka943 years ago

5 0

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf (\stackrel{x_1}{1}~,~\stackrel{y_1}{6}) ~\hspace{10em} \stackrel{slope}{m}\implies 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{3}(x-\stackrel{x_1}{1})\implies y - 6 = 3x-3 \\\\\\ y=3x+3\implies -3x+y=3\implies \stackrel{\textit{standard form}}{3x-y=-3}$

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Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :