Find an equation of the line that passes through the point (1,7) and is perpendicular to the line x−3y+16=0 in...
a.) Slope intercept form.
b.) General form.
If the line is perpendicular to x−3y+16=0, then their slopes must be the negative reciprocal of the other..
x−3y+16=0Add 3y3y=x+16Divide both sides by 3y=x3+163
By observation, the slope is 13, so the slope of the perpendicular line is m=−3
Thus,
y=mx+by=−3x+b
Solving for b at point (1,7)
7=−3(1)+bb=10
Therefore, the equation of the line is... y=−3x+10
b.) In general form
Ax+By+C=0y=−3x+10Add 3x and subtract 103x+y−10=0
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