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jasenka [17]
3 years ago
7

The graph of the equation y=−5x+b goes through the point A(5, −2). Find the value of b.

Mathematics
1 answer:
Furkat [3]3 years ago
5 0

\bf y=-5x+b\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\qquad \qquad \stackrel{therefore}{m=-5} \\\\[-0.35em] ~\dotfill\\\\


\bf A(\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})~\hspace{10em} slope = m\implies -5 \\\\\\ \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-(-2)=-5(x-5)\implies y+2=-5x+25 \\\\\\ y=-5x+25-2\implies y=-5x+\stackrel{\stackrel{b}{\downarrow }}{23}

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