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

Answer 1

To find the equation of a line perpendicular to another line, we need to find its slope. The given line has a slope of 3, since it is in the form y = mx + b, where m represents the slope.

A line perpendicular to this line will have a slope that is the negative reciprocal of 3. That is, it will have a slope of -1/3.

We need to find the equation of a line that passes through the point (6, -8) and has a slope of -1/3. We can start with the point-slope form of a linear equation:

y - y₁ = m(x - x₁),

where (x₁, y₁) represents the coordinates of the given point, and m represents the slope. Substituting in the values, we get:

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

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

y = (-1/3)x - 6.

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