How do you find the slope and intercept of #2x+3y=6#?

Answer 1

See below:

We can find the #x#-intercept by setting #y# equal to zero. We get
#2x=6=>x=3#
This is our #x#-intercept.
Similarly, we can set #x# equal to zero to find the #y#-intercept. We get
#3y=6=>y=2#
This is our #y#-intercept.

Next, we can convert this equation into slope-intercept form

#y=mx+b#, with slope #m#
We can start by subtracting #2x# from both sides to get
#3y=-2x+6#
Next, divide both sides by #3# to get
#y=-2/3x+2#
We see that our slope, the coefficient on #x# is #-2/3#.

Hope this helps!

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Answer 2

Slope: #-2/3#
x-intercept: #(3, 0)#
y-intercept: #(0, 2)#

#2x + 3y = 6#

To find the slope, first make the equation into slope-intercept form:

Subtract #color(blue)(2x)# from both sides of the equation:
#2x + 3y quadcolor(blue)(-quad2x) = 6 quadcolor(blue)(-quad2x)#

#3y = 6 - 2x#

Divide both sides by #color(blue)3#:
#(3y)/color(blue)3 = (6-2x)/color(blue)3#

#y = 2 - 2/3x#

We know that the slope is the value multiplied by #x#, meaning that the slope is #-2/3#.

#--------------------#

To find the x-intercept, plug in #0# for #y# and solve for #x#:
#0 = 2 - 2/3x#

Simplify:
#-2 = -2/3x#

#3 = x#

So the #x#-intercept is at #(3, 0)#.

#---------------------#

To find the y-intercept, plug in #0# for #x# and solve for #y#:
#y = 2 - 2/3(0)#

#y = 2 - 0#

#y = 2#

So the #y#-intercept is at #(0, 2)#.

Hope this helps!

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Answer 3

To find the slope and intercept of the equation 2x + 3y = 6:

  1. Solve the equation for y to put it in slope-intercept form (y = mx + b).
  2. Subtract 2x from both sides: 3y = -2x + 6.
  3. Divide both sides by 3 to isolate y: y = (-2/3)x + 2.
  4. The slope (m) of the line is the coefficient of x, which is -2/3.
  5. The y-intercept (b) of the line is the constant term, which is 2.
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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.

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