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

y =3x - 7

Explanation:

Answer 2

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
`(-1)/(3)`

This means that the slope of a line perpendicular to y = 3x - 7 is
`(-1)/(3)`

This is the current formula you found:

`y=(-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 =
`(-1)/(3)`(2) + b

-1 =
`(-2)/(3)` + b

`(-1)/(3)` = b

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

y =
`(-1)/(3) x - (1)/(3)`

Hope this helped!

~Just a girl in love with Shawn Mendes