Answer: x + 3y = 2
Step-by-step explanation:
Given:
y - 3 = 3 ( x + 1 )
y - 3 = 3x + 3
y = 3x + 3 + 3
y = 3x +6
comparing the equation with the formula for finding equation of line in slope - intercept form
y = mx + c , where m is the slope and c is the y - intercept. This means that the slope of the line above is 3
Two lines are said to be perpendicular if the product of their slope = -1, that is , if [tex]m_{1}[/tex] is the slope of the first line and [tex]m_{2}[/tex] is the slope of the second line , if they are perpendicular , then [tex]m_{1}[/tex][tex]m_{2}[/tex] = -1
Considering this rule , this means that the slope of the line we are to find = [tex]\frac{-1}{3}[/tex]
Using the formula : y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) to find the equation of the line , we have
y - (-1 ) = [tex]\frac{-1}{3}[/tex] ( x - 5 )
y + 1 = [tex]\frac{-1}{3}[/tex] ( x - 5 )
multiplying through by 3 , we have
3 ( y + 1 ) = -1 ( x - 5)
Expanding , we have
3y + 3 = -x + 5
writing the equation in standard form , we have
3y + x = 5 - 3
Therefore :
x + 3y = 2
