Perpendicular Graphing #18

Question

Write the equation of the line in slope intercept form that is perpendicular to 3x-2=5 and passes through (-6,4).

 

Please explain like you are teaching i have no idea what i am doing thanks in advanced.

Answer 1

The equation  3x - 2y = 5  is in Standard Format.

 

To see the slope easily, convert this to slope-intercept form (y=mx+b  where m= slope):

    3x - 2y = 5

         -2y = -3x + 5          [subtract 3x from both sides]

       y = (3/2)x - 5/2          [divide both sides by (-2)]

 

This line has a slope of (3/2).  All lines perpendicular to it have a slope of (-2/3), that is, the negative reciprocal (-1/m).

The perpendicular line has the formula  y = (-2/3) + b  and we need point (-6,4) to find b.

     4 = (-2/3)(-6) + b

     4 = 4 + b

     0 = b

 

The perpendicular line has the formula:  y = (-2/3)x

Answer 2

So, Alissa, first we need to find the slope. Remember the firm y = mx + b, where m is the slope and b is the y-intercept.

 

3x - 2y = 5

-2y = -3x + 5

y = (3/2)x - 5/2

 

So, the slope of our line is 3/2. Perpendicular lines have opposite, reciprocal slopes, so our new line has a slope of -2/3.

 

Now, we have a form...

 

(y - y₁) = m(x - x₁)

 

x₁ and y₁ come from the given point.

 

(y - 4) = (-2/3)(x -(-6))

y - 4 = (-2/3)x - 4

y = (-2/3)x

 

Hope this helps!