Answer:
y = -1/2x - 3
Explanation:
Step 1: Find the slope of the line y - 4 = 2(x - 6):
- The slopes of perpendicular lines are negative reciprocals of each other as shown by the following 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.
The line y - 4 = 2(x - 6) is in the point-slope form of a line, whose general equation is given by:
y - y1 = m(x - x1), where
- (x1, y1) are one point on the line (the opposite sign of the points are used in this form so for example, the actual y-coordinate on the line is 4 and not -4 while an actual x-coordinate on the line is 6 and not -6),
- and m is the slope.
Thus, the slope of the line y - 4 = 2(x - 6) is 2.
Step 2: Find the slope (m2) of the other line:
Now we can find the slope of the other line (m2) by plugging in 2 for m1:
m2 = -1 / 2
m2 = -1/2
Thus, the slope of the other line is -1/2
Step 3: Find the y-intercept (b) of the other line.
The general equation of the slope-intercept form of a line is given by:
y = mx + b, where
- (x, y) is any point on the line,
- m is the slope,
- and b is the y-intercept.
Thus, we can find b, the y-intercept, of the line by plugging in -1/2 for m, and (-2, -2) for (x, y) in the slope-intercept form:
-2 = -1/2(-2) + b
-2 = 1 + b
-3 = b
Thus, the y-intercept is -3.
Therefore, the equation of the line in slope-intercept form that is perpendicular to the line y - 4 = 2(x - 6) and passes through (-2, -2) is y = -1/2x - 3.