Answer:
Equation of the line: y = 1/2x - 4
Explanation:
Identifying the form of y = -2x + 8:
- Knowing the form of y = -2x + 8 will be helpful in finding the equation of the other line.
y = -2x + 8 is in the slope-intercept form of a line, whose general equation is given by:
y = mx + b, where:
- m is the slope,
- and b is the y-intercept.
Thus, the slope of y = -2x + 8 is -2 and the y-intercept is 8.
Relationship between the slopes of perpendicular lines:
- The slopes of perpendicular lines are negative reciprocals of each other.
We can represent this with the equation 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 (i.e., -2):
Finding m2:
Now, we can find m2 by substituting -2 for m1 in the perpendicular slope formula above:
m2 = -1 / -2
m2 = 1/2
Thus, the slope of the other line is m2.
Finding the y-intercept (b) of the other line and writing its equation:
Since the other line passes through (4, -2) and has a slope of 1/2, we can find its y-intercept (b) by substituting (4, -2) for (x, y) and 1/2 for m in the slope-intercept form:
-2 = 1/2(4) + b
(-2 = 2 + b) - 2
-4 = b
Therefore, y = 1/2x - 4 is the equation of the line that contains the point (4, -2) and is perpendicular to the line y = -2x + 8.