How do you write the equation of line passes through (-2,-2), and is perpendicular to y= -1/3x + 9?

Answer 1

#y=3x+4#

#"given the slope of a line m then the slope of a line"# #"perpendicular to it is"#
#•color(white)(x)m_(color(red)"perpendicular")=-1/m#
#"the equation of a line in "color(blue)"slope-intercept form"# is.
#•color(white)(x)y=mx+b#
#"where m is the slope and b the y-intercept"#
#y=-1/3x+9" is in this form with "m=-1/3#
#rArrm_(color(red)"perpendicular")=-1/(-1/3)=3#
#rArry=3x+blarrcolor(blue)"is the partial equation"#
#"to find b substitute "(-2,-2)" into the partial equation"#
#-2=-6+brArrb=4#
#rArry=3x+4larrcolor(red)"equation of perpendicular line"#
Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To write the equation of a line that is perpendicular to a given line, you need to find the negative reciprocal of the slope of the given line. The given line has a slope of -1/3, so the perpendicular line will have a slope of 3.

Now that we have the slope of the perpendicular line, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given the point (-2, -2) and the slope 3, we can substitute these values into the point-slope form to get the equation of the perpendicular line:

y - (-2) = 3(x - (-2))

Simplify:

y + 2 = 3(x + 2)

Distribute:

y + 2 = 3x + 6

Subtract 2 from both sides to isolate y:

y = 3x + 4

So, the equation of the line that passes through (-2, -2) and is perpendicular to y = -1/3x + 9 is y = 3x + 4.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7