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Which of these is a point slope equation of the line that is perpendicular to y-8=3(x-10) and passes through (-2,7)?

1 Answer

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Answer:

The point slope form is:
y-7=-(1)/(3) \,(x+2)

Explanation:

Recall the general point-slope form of a line of slope "m" and going through a point
(x_0,y_0), is given by:
y-y_0=m(x-x_0)

Notice therefore, that the given line is expressed in "point-slope" form


y-8=3(x-10)

where the slope is given by the value: "3".

Recall that the slope of a line perpendicular to another given line of known slope "m" is the "opposite of the reciprocal" of that "m". That is:


m_(perp)=-(1)/(m)

Then for our case, the line perpendicular to the one given, must have slope given by:


m_(perp)=-(1)/(m)=-(1)/(3)

So now we can create easily the point-slope form of the requested perpendicular line that goes through the point (-2,7) using the general point-slope form mentioned above:


y-y_0=m(x-x_0)\\y-7=-(1)/(3) \,(x-(-2))\\y-7=-(1)/(3) \,(x+2)

User Frankgreco
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