Plans for a stadium are drawn on a coordinate grid. One wall lies on the line y = 3x + 2. A perpendicular wall passes through the point (6, -8.) Write the equation of the line that contains the new wall

Answer 1

To find the equation of the line that contains the new wall, we need to determine its slope and y-intercept.

The given line, y = 3x + 2, has a slope of 3. Perpendicular lines have slopes that are negative reciprocals of each other. Therefore, the slope of the new wall is -1/3.

To find the y-intercept, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a known point on the line.

Using the point (6, -8) and the slope -1/3, we have:

y - (-8) = (-1/3)(x - 6)
y + 8 = (-1/3)(x - 6)

To simplify the equation, we can distribute the -1/3:

y + 8 = (-1/3)x + 2

Finally, we can isolate y by subtracting 8 from both sides:

y = (-1/3)x - 6

Therefore, the equation of the line that contains the new wall is y = (-1/3)x - 6.