Answer:
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)
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)