Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y = 3x – 3. A perpendicular brace passes through the point (–7, 9). Write an equation of the line that contains the brace.

Using the slope intercept formula, we conclude that the slope of line p:y=3x-3 is 3.Since line k is perpendicular to line p it must have a slope that is the negative reciprocal.Therefore the slope of line k is -1/3.Using the formula y-9=-1/3(x-(-7)) and doing the math we will end up with k:y=-1/3x+34/3

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mominetti mominetti · Answer 2 · 2019-09-11T13:34:38+02:00

Answer:

The answer is:

[tex]y = -\frac{1}{3}x +\frac{20}{3}[/tex]

Step-by-step explanation:

The slope of line y = 3x - 3 is k = 3, so the negative reciprocal is given by -1/k. Therefore the slope for the perpendicular equation is -1/3.

Now, the perpendicular equation passes through the point x = -7 y = 9, so you need to find b:

[tex]y = -\frac{1}{3}x +b[/tex] // replace y = 9 and x = -7

[tex]9 = -\frac{-7}{3} +b[/tex] // substract 7/3 in both sides

[tex]9 - \frac{7}{3} = \frac{7}{3} - \frac{7}{3} + b[/tex] // solve

[tex]\frac{20}{3} = b[/tex]

Replace b in the equation:

[tex]y = -\frac{1}{3}x +\frac{20}{3}[/tex]

See the attachment.