To answer this you must know the rule for the slopes of perpendicular lines. the rule is that if 2 lines are perpendicular to each other, then their slopes are opposite reciprocal.
the word opposite means that if the slope of one is positive, then the other is negative. And vice versa.
the word reciprocal means that you divide 1 by whatever the slope is. So the reciprocal of x is 1/x.
so let's say we have a slope of -2 and what to find a line perpendicular. We need to find the opposite reciprocal. the opposite of -2 is 2. And the reciprocal of 2 is 1/2. So perpendicular line would have slope of 1/2
now to answer yours.
We know that y = mx + b, where m = slope and b = y intercept.
so: y - 3 = 4 (x + 2) y = 4x + 11
so m = 4. the slope is 4.
the opposite of 4 is - 4 and the reciprocal of - 4 is - 1/4. So that is out new slope of perpendicular line.
We know that given a point we can use: (y - y1) = m (x - x1), where (x1, y1) is the given point
We are given point (- 5, 7) and we know m = - 1/4. so:
y - (7) = - 1/4(x - (- 5)) y - 7 = - 1/4(x + 5) y - 7 =- 1/4x - 5/4 y = - 1/4x + 23/4
this should be equAtion. We can check by seeing if slopes are opposite reciprocal and by plugging in point.
- 1/4 is opposite reciprocal of 4.
plug in point 7 = - 1/4 (- 5) + 23/4 7 = 5/4 + 23/4 7 = 7
