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

To find the equation of a line perpendicular to y = -14x + 3 and passing through (2, 6), use the negative reciprocal of the slope of line a. Plug in the values into the point-slope form of a linear equation to find the equation of line b.

Step-by-step explanation:

To find the equation of a line that is perpendicular to y = -14x + 3 and passes through the point (2, 6), we can use the fact that perpendicular lines have slopes that are negative reciprocals of each other.

First, we need to determine the slope of line a. The equation is in the form y = mx + b, where m is the slope. In this case, m = -14.

Since line b is perpendicular to line a, the slope of line b will be the negative reciprocal of -14.

The negative reciprocal of -14 is 1/14.

Now we can use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1).

Plugging in the values (2, 6) and m = 1/14, we get:

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

Simplifying the equation gives us the equation of line b:

y = (1/14)x + 6/7

Answer 2

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 ...