Question

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.

Answer 1

The answer is:

`y = -(1)/(3)x +(20)/(3)`

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:

`y = -(1)/(3)x +b` // replace y = 9 and x = -7

`9 = -(-7)/(3) +b` // substract 7/3 in both sides

`9 - (7)/(3) = (7)/(3) - (7)/(3) + b` // solve

`(20)/(3) = b`

Replace b in the equation:

`y = -(1)/(3)x +(20)/(3)`

See the attachment.

Answer 2

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