Question 201411: Find an equation of the the line satisfying the given conditions.
Through (2, 8); perpendicular to 9x + 7y = 74
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! Find an equation of the the line satisfying the given conditions.
Through (2, 8); perpendicular to 9x + 7y = 74
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First, find the slope of:
9x + 7y = 74
Do this by putting it into the "slope-intercept" form:
7y = -9x + 74
y = (-9/7)x + 74/7
Therefore, slope = -9/7
.
If a line is perpendicular, we need the negative reciprocal of the slope above:
Our new slope is then 7/9
Use the slope (7/9) and the given point (2,8) and plug it into the "point-slope" form:
y-y1 = m(x-x1)
y-8 = 7/9(x-2)
y-8 = 7/9(x) - 14/9
y = 7/9(x) - 14/9 + 8
y = 7/9(x) - 14/9 + 72/9
y = 7/9(x) + 58/9 (slope-intercept form of new line)
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