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

1 answer:

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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Answer: $\sqrt{2}/2$ which is Choice B

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Explanation:

Refer to the unit circle below. I've highlighted the angle 45 degrees and its corresponding sine value. It's the y coordinate of the point on the unit circle, for this particular angle.

Therefore, $\sin(45^{\circ}) = \frac{\sqrt{2}}{2}$

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You could alternatively draw out a 45-45-90 triangle. Let x be the leg length and the hypotenuse is 1 unit long. Solve $x^2+x^2 = 1$ for x and you should get $x = \frac{\sqrt{2}}{2}$ as the length of each leg.