Question

What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, −1)? y = x − y = x − y = 3x − 3 y = 3x − 7

Answer 1

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 $\frac{-1}{3}$

This means that the slope of a line perpendicular to y = 3x - 7 is $\frac{-1}{3}$

This is the current formula you found:

$y=\frac{-1}{3} x + b$

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 = $\frac{-1}{3}$(2) + b

-1 = $\frac{-2}{3}$ + b

$\frac{-1}{3}$ = b

That means that the equation perpendicular to y = 3x - 7 is...

y = $\frac{-1}{3} x - \frac{1}{3}$

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer 2

Answer:

y =3x - 7

Step-by-step explanation: