Given line: y =3x - 7
Slope-intercept form is y = mx + b where m is slope and b is the y intercept
To find m you must take the slope of the line given, which would be 3, and take its opposite reciprocal (switch its sign to negative/positive if it was originally positive/negative and flip the numerator and denominator)
the opposite of 3 is -3 and the reciprocal of -3 is [tex]\frac{-1}{3}[/tex]
This means that the slope of a line perpendicular to y = 3x - 7 is [tex]\frac{-1}{3}[/tex]
This is the current formula you found:
[tex]y=\frac{-1}{3} x + b[/tex]
To find the y-intercept (b) in the point that this line goes through (2, -1) into the x and y of the equation and solve for b
-1 = [tex]\frac{-1}{3}[/tex](2) + b
-1 = [tex]\frac{-2}{3}[/tex] + b
[tex]\frac{-1}{3}[/tex] = b
That means that the equation perpendicular to y = 3x - 7 is...
y = [tex]\frac{-1}{3} x - \frac{1}{3}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
