How do you find a standard form equation for the line that is perpendicular to #6x-2y+5=0# and has the same y-intercept as #x-y+8=0#?
When given an equation of a line of the form:
The family of perpendicular lines are of the form:
Where k is an unknown constant.
The family of perpendicular lines are:
We must find the y intercept of the line
Substitute the point
Substitute this into equation :
Equation  is the answer.
This is the same as:
This can be written as:
So the y-intercept for this equation is 8.
Thus the equation we are looking for passes through the point:
Consider the given equation:
Divide both sides by 2
Thus the gradient (slope) for
A line that is perpendicular to it will have the gradient of:
Thus our standardised form for the new line is:
So the equation of the perpendicular line is: