Question

The equation of line a is y=−14x+3. If line b runs perpendicular to line a and passes through (2, 6), what would be the equation of line b?

Answer 1

Hint : The product of the slopes of two lines perpendicular to each other is - 1 .

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In slope-intercept ( y = ax + b ) from of the linear equations the coefficient of x is the slope of the line.

Thus :

Slope of line a = - 14

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Suppose that the slope of line b is x according to the Hint we have :

- 14 × x = - 1

negatives simplify

14x = 1

Divide both side by 14

14x ÷ 14 = 1 ÷ 14

x = 1/14

So the slope of line b is 1/14

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Now let's find the equation of line b by point-slope formula using the point question have us ( 2 , 6 ) :

y - y( given point ) = Slope × ( x - x ( g p ) )

y - 6 = 1/14 × ( x - 2 )

y - 6 = 1/14 x - 2/14

y - 6 = 1/14 x - 1/7

Add both sides 6

y - 6 + 6 = 1/14 x - 1/7 + 6

y = 1/14 x - 1/7 + 42/7

y = 1/14 x + 41/7

And we're done ...