Question

Plans for a bridge are drawn on a coordinate grid. One girder of the bridge lies on the line y = 3x-5. A perpendicular brace passes through the point (5, +7). Write an equation of the line that contains the brace.

Answer 1

To find the equation of the line that contains the brace, we need to determine its slope, which is the negative reciprocal of the given girder's slope. Using the point-slope form, we can write the equation of the line that contains the brace as y - y1 = m(x - x1), where (x1, y1) is the given point (5, 7) and m is the slope (-1/3). The equation of the line that contains the brace is y = (-1/3)x + 22/3.

Step-by-step explanation:

To find the equation of the line that contains the brace, we need to determine its slope. Since the brace is perpendicular to the given girder, its slope will be the negative reciprocal of the girder's slope. The girder has a slope of 3, so the brace's slope will be -1/3.

Using the point-slope form, we can write the equation of the line that contains the brace as y - y1 = m(x - x1), where (x1, y1) is the given point (5, 7) and m is the slope (-1/3):

y - 7 = (-1/3)(x - 5)

Simplifying, we get y - 7 = (-1/3)x + 5/3

Rearranging the equation, we have y = (-1/3)x + 22/3. Therefore, the equation of the line that contains the brace is y = (-1/3)x + 22/3.