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.
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.
To find the equation of the line that contains the new wall, we need to determine its slope and use the point-slope formula.
1. Start with the given equation of one of the walls: y = 3x + 2. This equation represents the line that the first wall lies on, with a slope of 3.
2. Since the new wall is perpendicular to the given line, its slope will be the negative reciprocal of 3. The negative reciprocal of 3 is -1/3.
3. We also know that the new wall passes through the point (6, -8).
4. Now, let's use the point-slope formula to write the equation:
y - y1 = m(x - x1), where (x1, y1) is the given point, and m is the slope.
Substituting the values, we have:
y - (-8) = -1/3(x - 6)
y + 8 = -1/3x + 2
5. Simplify the equation:
y = -1/3x + 2 - 8
y = -1/3x - 6
Therefore, the equation of the line that contains the new wall is y = -1/3x - 6.
To write the equation of the line that contains the new wall, we need to find the slope of the new wall first.
The given perpendicular wall passes through the point (6, -8). We know that any line perpendicular to y = 3x + 2 will have a slope that is the negative reciprocal of the slope of y = 3x + 2.
The slope of y = 3x + 2 is 3. So the slope of the perpendicular line will be -1/3.
Now, we have the slope (-1/3) and a point (6, -8) on the line. We can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope.
Substituting the values,
y - (-8) = (-1/3)(x - 6)
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.