Respuesta :
Answer:
7x + 3y = 44
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 = 5 into this form by adding 3x to both sides
7y = 3x + 5 ( divide all terms by 7 )
y = [tex]\frac{3}{7}[/tex] x + [tex]\frac{5}{7}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{3}{7}[/tex]
Given a line with slope m then 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
To find c substitute (5, 3) into the partial equation
3 = - [tex]\frac{35}{3}[/tex] + c ⇒ c = 3 + [tex]\frac{35}{3}[/tex] = [tex]\frac{44}{3}[/tex]
y = - [tex]\frac{7}{3}[/tex] x + [tex]\frac{44}{3}[/tex] ← in slope- intercept form
Multiply through by 3
3y = - 7x + 44 ( add 7x to both sides )
7x + 3y = 44 ← in standard form
Answer:
equation: y = -7/3x + 14 2/3
Step-by-step explanation:
–3x+7y=5
y = 3/7 x + 5
slope of perpendicular line: - 7/3
y = mx + b for (5 , 3)
b = y - mx = 3 - ((-7/3) * 5) = 3 + 35/3 = 44/3 = 14 2/3
equation: y = -7/3x + 14 2/3
