Respuesta :
Answer:
y = - [tex]\frac{1}{3}[/tex] x + 6
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 )
y = 3x + 2 ← is in slope- intercept form
with slope m = 3
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}{3}[/tex], thus
y = - [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (3, 5) into the partial equation
5 = - 1 + c ⇒ c = 5 + 1 = 6
y = - [tex]\frac{1}{3}[/tex] x + 6 ← equation of perpendicular line
Answer:
x -3y -18=0
Step-by-step explanation:
To find the equation of the straight line passing through the point (3,5) which is perpendicular to the line y = 3x + 2, we will first find the slope(m).
To find the slope m of the perpendicular equation;
y = 3x + 2 --------------(1)
comparing the equation above with the standard equation of a circle
y=mx + c
m=3
The slope of perpendicular equation;
[tex]m_{1}m_{2}[/tex] = -1
3[tex]m_{2}[/tex] = -1
Divide both-side of the equation by 3
[tex]m_{2}[/tex] = -1/3
so, the slope of our perpendicular equation is -1/3
Then, we go ahead to find our intercept
To find the intercept, we will plug in the points and the new slope into the formula y =mx + c
5 = -[tex]\frac{1}{3}[/tex](3) + c
5 = -1 +c
Add one to both-side of the equation
5+1 = -1 + c + 1
6 =c
c=6
our intercept c is equal to 6
so we can now proceed to form our equation.
y = -[tex]\frac{1}{3}[/tex] x + 6
Multiply through by 3
-3y = -x + 18
We can rearrange the equation, hence;
x -3y -18=0
Therefore the equation of the straight line that passes through the point (3,5) which is perpendicular to the line y = 3x + 2 is x -3y -18=0
