What is the equation of a line that goes through #(-6, 3)# and has a slope of #-2/3#?

Answer 1

#y= -2/3x-1#

Use

#y=mx+b#

Plug in the numbers

#3=-2/3(-6)+b#

Solve

#3=4+b#
Subtract #4# from both sides
#-1=b#

So

#y=-2/3x-1#
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

The equation of the line can be expressed in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept. Given that the slope (m) is -2/3 and a point on the line is (-6, 3), we can substitute these values into the equation and solve for the y-intercept (b).

Using the point-slope form: y - y₁ = m(x - x₁), where (x₁, y₁) = (-6, 3), and m = -2/3:

y - 3 = (-2/3)(x - (-6)) y - 3 = (-2/3)(x + 6) y - 3 = (-2/3)x - 4 y = (-2/3)x - 4 + 3 y = (-2/3)x - 1

Therefore, the equation of the line is y = (-2/3)x - 1.

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 3

The equation of the line passing through the point (-6, 3) with a slope of -2/3 is:

[ y - y_1 = m(x - x_1) ]

Where ( (x_1, y_1) ) is the given point and ( m ) is the slope.

Substituting the given values:

[ y - 3 = -\frac{2}{3}(x + 6) ]

Now, simplify the equation:

[ y - 3 = -\frac{2}{3}x - 4 ]

[ y = -\frac{2}{3}x - 1 ]

So, the equation of the line is ( y = -\frac{2}{3}x - 1 ).

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