Answer:
7x - 3y = 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 3x + 7y = 15 into this form
Subtract 3x from both sides
7y = - 3x + 15 ( divide all terms by 7 )
y = - x +
← in slope- intercept form
with slope m = -
Given a line with slope m the the slope of a line perpendicular to it is
= -
= -
=
, thus
y = x + c ← is the partial equation of the line
To find c substitute (4, 9) into the partial equation
9 = + c ⇒ c -
y = x -
← in slope- intercept form
Multiply through by 3
3y = 7x - 1 ( subtract 3y from both sides )
0 = 7x - 3y - 1 ( add 1 to both sides )
1 = 7x - 3y, that is
7x - 3y = 1 ← in standard form