Answer:
Line v equation: y = -2x + 3
Explanation:
Relationship between the slopes of perpendicular lines:
- The slopes of perpendicular are negative reciprocals of each other.
This is shown by the formula m2 = -1 / m1, where:
- m2 is the slope of the line we're trying to find,
- and m1 is the slope of the line we're given.
Identifying the form of x - 2y = 20 and converting to slope-intercept form:
x - 2y = 20 is in the standard form of a line, whose general equation is given by:
Ax + By = C, where:
- A, B, and C are constants.
The general form of the slope-intercept form is given by:
y = mx + b, where:
- m is the slope,
- and b is the y-intercept.
Thus, we can convert x - 2y = 20 to slope-intercept form by isolating y:
(x - 2y = 20) - x
(-2y = -x + 20) / -2
y = 1/2x - 10
Thus, the slope of line u is 1/2.
Finding the slope of line v:
Now, we can find the slope of line v by substituting 1/2 for m1 in the perpendicular slope formula:
m2 = -1 / (1/2)
m2 = -1 * 2
m2 = -2
Thus, the slope of line v is -2.
Finding the y-intercept of line v and finding the equation of line v (in slope-intercept form):
Now, we can find the y-intercept of line v by substituting (3, -3) for (x, y) and -2 for m in the slope-intercept form:
-3 = -2(3) + b
(-3 = -6 + b) + 6
3 = b
Thus, the y-intercept of ilne v is 3.
Therefore, the equation of line v (in slope-intercept form) is y = -2x + 3.