First find the slope of the line .

Apply subtraction property of equality: If a = b than a – c = b – c.

      (Subtract 3x from each side)

                   (Apply additive inverse property: )

\

Apply multiplication property of equality: If a = b than a c = b  c c  0.

  (Multiply each side by negative 5)

                       (Cancel common terms)

The line in slope-intercept form , where m is slope and b is y-intercept.

Compare the equation with slope-intercept form and find the slope of the line.

= 15

If two lines are perpendicular, the slope (m₁) of one line is opposite reciprocal of the second line slope (m₂). It can be represented as, .

Slope of the line perpendicular to given line is 

So, slope of the new line = .

The line equation in slope-intercept form is , where m is the slope and b is the y-intercept.

First find the y-intercept value.

                    (Substitute for m)

              (Substitute 6, –5 for x, y)

                      (Multiply: )

Apply addition property of equality: If a = b than a + c = b + c.

     (Add  to each side)

                          (Apply additive inverse property: )

                             (Add: )

Substitute for m and for b in the Slope-intercept form line equation.

The line equation in slope-intercept form is .