Question

Find the equation of the line which is perpendicular to the line y=− 1/3x+6 through the point (2,4).

Answer 1

Answer:

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.