Question

Find an equation of the line that contains the given point and is perpendicular to the given line. Using a graphing calculator to verify the result.
(-9,12), 5x-6y=7

Answer 1

The equation of the line is y=2x+1.

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=− 3/6x+ 5/6

​y=− 1/2x+ 5/6

​The slope of our first line is equal to − 1/2.Perpendicular lines have negative reciprocal slopes, so if the slope of one is x, the slope of the other is − 1/x

​The negative reciprocal of − 1/2 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.

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