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 = - [tex]\frac{3}{7}[/tex] x + [tex]\frac{15}{7}[/tex] ← in slope- intercept form
with slope m = - [tex]\frac{3}{7}[/tex]
Given a line with slope m the the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{7} }[/tex] = [tex]\frac{7}{3}[/tex], thus
y = [tex]\frac{7}{3}[/tex] x + c ← is the partial equation of the line
To find c substitute (4, 9) into the partial equation
9 = [tex]\frac{28}{3}[/tex] + c ⇒ c - [tex]\frac{1}{3}[/tex]
y = [tex]\frac{7}{3}[/tex] x - [tex]\frac{1}{3}[/tex] ← 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
