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
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.
To find the equation of the new wall, we first need to determine its slope. Since the new wall is perpendicular to the line y = 3x + 2, we know that the slopes of the two lines are negative reciprocals of each other.
The slope of the given line y = 3x + 2 is 3. The negative reciprocal of 3 is -1/3.
Now, we can use the point-slope form of a linear equation to determine the equation of the new wall. The point-slope form is given as:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and m is the slope.
Using the point (6, -8) and the slope -1/3, we have:
y - (-8) = (-1/3)(x - 6)
Simplifying:
y + 8 = (-1/3)x + 2
Re-arranging the equation:
y = (-1/3)x + 2 - 8
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 first need to determine the slope of the perpendicular line.
The given wall has a slope of 3. Perpendicular lines have negative reciprocal slopes, meaning the slope of the new wall will be -1/3.
Now we have the slope (-1/3) and a point (6, -8) that lies on the line. We can use the point-slope form of the equation of a line to find the equation of the line that contains the new wall.
The point-slope form of a line is: y - y₁ = m(x - x₁), where (x₁, y₁) are the coordinates of a point on the line and m is the slope of the line.
Using the coordinates (6, -8) and the slope -1/3, we can substitute these values into the point-slope form:
y - (-8) = (-1/3)(x - 6)
Simplifying, we have:
y + 8 = (-1/3)(x - 6)
To write the equation in standard form, we multiply through by -3 to eliminate the fraction:
-3(y + 8) = x - 6
Distributing -3 on the left side:
-3y - 24 = x - 6
Rearranging the equation by moving x and 3y to the left side:
x - 3y = 18 - 24
Combining like terms:
x - 3y = -6
Therefore, the equation of the line that contains the new wall is x - 3y = -6.