Which of the following equations of a line perpendicular to the line y=-1/3x+1 , passing through the point (2,7)?

y=3x+1  (slope-intercept form)

-3x+y=1 (standard form)

3x-y=-1 (another version of standard form)

y-7=3(x-2) (point-slope form)

Step-by-step explanation:

y=mx+b is slope intercept form where m is slope and b is y-intercept.

The slope of perpendicular lines are opposite reciprocals.

The opposite reciprocal of -1/3 is 3.

So we are looking for a line of the form y=3x+b going through (2,7)

y=3x+b with (x,y)=(2,7)

7=3(2)+b

7=6+b

7-6=b

1=b

b=1

So the equation is y=3x+1.

Now you can also put it in standard form:

Subtract 3x on both sides:

-3x+y=1

You can also multiply both sides by -1:

3x-y=-1

ax+by=c is standard form.

We can also use point slope form.

y-y1=m(x-x1) where (x1,y1) is a point contained by our line and m is the slope.

We have m=3 and (x1,y1)=(2,7)

y-7=3(x-2)

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