Which equation represents a line that passes through (–2, 4) and has a slope of 2/5 ?

1 answer:

3 0

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ -2}}\quad ,&{{ 4}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{2}{5}
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-4=\cfrac{2}{5}[x-(-2)]
\implies 
y-4=\cfrac{2}{5}(x+2)
\\\\\\
y-4=\cfrac{2}{5}x+\cfrac{4}{5}\implies y=\cfrac{2}{5}x+\cfrac{4}{5}+4\implies y=\cfrac{2}{5}x+\cfrac{24}{5}$

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