Given equation of line y=−3x+5.
On comparing with slope-intercept form y=mx+b, we can see that m=-3.
So the slope of the given line is -3.
We are given that lines are perpendicular.
Slopes of perpendicular line are reciprocal and opposite in sign.
We got slope of given line -3. The reciprocal of -3 is -1/3 and opposite sign of -1/3 would be 1/3.
So, the slope of the required equation of line would be 1/3.
We are given a point (2, 6).
We got a point and slope. So we can apply point-slope form directly.
y-y1 = m(x-x1)
y-6 = 1/3 (x-2).
Distributing 1/3 on right side.
y-6 = 1/3 x - 3/2
Adding 6 on both sides, we get
y-6+6 = 1/3 x - 3/2 +6
Simplifying fractions -3/2+6 by taking common denominator, we get
-3/2+6/1 = -3/2 + 12/2 = (-3+12)/2 = 9/2
Therefore, the required equation will be
y = 1/3 x +9/2
