We must must transform the standard form equation 3x+6y=5 into a slope-intercept form equation (y=mx+b) to find its slope.
3x+6y=5 (Subtract 3x on both sides.)
6y=−3x+5 (Divide both sides by 6.)
y=−
6
3
x+
6
5
y=−
2
1
x+
6
5
The slope of our first line is equal to −
2
1
. Perpendicular lines have negative reciprocal slopes, so if the slope of one is x, the slope of the other is −
x
1
.
The negative reciprocal of −
2
1
is equal to 2, therefore 2 is the slope of our line.
Since the equation of line passing through the point (1,3), therefore substitute the given point in the equation y=2x+b:
3=(2×1)+b
3=2+b
b=3−2=1
Substitute this value for b in the equation y=2x+b:
y=2x+1
Hence, the equation of the line is y=2x+1.
