what's the slope and the y intercept ? 12x - 4y + 8 = 0 teacher won't explain it well :/

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ishpiro | College Teacher | (Level 1) Educator

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There are different ways to find the slope and intercept of a line. One of them is rewriting the given equation in slope-intercept form.

The slope-intercept forms looks like y = mx + b. Then, m, the number in front of x, is the slope, and b,  the number added to mx, is the y-intercept.

To rewrite the equation in slope-intercept form, solve for y in terms of x:

12x - 4y + 8 = 0.

The goal is to isolate y, so subtract both 12x and 8 from both sides:

-4y = -12x - 8

Now divide both sides of the equation by  - 4:

`y = (-12)/-4 x - 8/-4` 

`y = 3x - (-2)`

`y=3x+2`

Comparing this to the slope-intercept form y = mx + b, we see that the slope, m, is m = 3 and the y-intercept, b, is b = 2.

The slope is 3 and the intercept is 2.

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baxthum8 | High School Teacher | (Level 3) Associate Educator

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What is the slope and y-intercept of `12x-4y+8=0` ?

In order to determine the slope and y-intercept you will want to change the equation to slope-intercept form.  This is: `y=mx+b` where m represents the slope and b represents the y-intercept.

Solve the equation for y.

`12x-4y+8=0` First move all terms not including the y-term to the right side of the = sign.  First subtract 8 from each side. 

This gives:  `12x-4y = -8` .  Next subtract 12x from each side.

This gives: `-4y=-12x-8` .  Now divide all terms by -4.

This gives: `y=3x+2` Now that the equation is in slope-intercept form, `y=mx+b` you can see that the slope is 3 and the y-intercept is 2 or (0, 2)

Sources:
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steamgirl | Student, College Junior | (Level 1) Honors

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Alright, whenever you're working with a function, first put it into standard form (y=mx+b):

12x - 4y + 8 = 0

12x + 8 = 4y

3x + 2 = y

or y = 3x +2. Now look back at your definition of standard form, the m in the equation in the slope of the line, now you can graph & do the whole rise over run equation if your unsure, but that will still get you m in every instance. So the slope for this equation is 3. The y intercept is anywhere on the graph where the function crosses the y-axis, or when x is equal to zero. Therefore, plug zero into the equation for x and whatever is left after solving is your y-intercept, in this case (0,2).

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rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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To find the slope and y intercept, you must change your equation to standard form. The standard form of a linear equation is y=mx+b, where m represents slope and b represents the y-intercept.

Your goal is to get y by itself

12x - 4y + 8 = 0                  The easiest way to do this is add 4y to both sides

12x+8=4y                           Now divide by 4

(12x/4)+(8/4)                      Simplify

3x+2=y

Your slope is 3 and your y-intercept is positive 2.

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acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

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y=mx+b is the original form 

12x - 4y + 8 = 0

-4y= -12x -8

divide by -4

y= 3x+2

where 3 is the slope and 2 is the y intercept. 

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ayl0124 | Student, Grade 12 | (Level 1) Valedictorian

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When looking for the slope and the y-intercept, your immediate thought should be the equation: `y = mx + b` . So to find the slope and the y-intercept, you simply have to adjust the equation to look like that slope-intercept form.

`12x - 4y + 8 = 0`

Make sure that the two variables are on different sides of the equation from each other. That means that you should add 4y to both sides of the equation.

`12x + 8 = 4y`

You want y to have no coefficients, so just divide by four.

`3x + 2 = y`

Now that you have your original equation in slope-intercept form, you can now interpret the equation. "m" is the slope, while "b" is the y-intercept. 

Thus, m = 3 and b = 2, so the slope is 3 and the y-intercept is 2.

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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the slope formula is y=mx+b 

The first step to solving this problem would be to set up the problem into y=mx+b form.

12x - 4y + 8 = 0

First we must add the opposite of each number, so they cancel until y -4y is left alone.

for example to cancel out 8 we must add -8 to both sides.

12x - 4y + 8 = 0

              -8    -8

12x-4y=-8

now minus 12x

12x - 4y = -8

-12x          -12x

-4y=- 12x - 8

our goal is to get y by itself so divide by -4

`(-4y)/(-4) = (-12x)/(-4)- (8)/-4 `

y=3x+2

the slope is 3 and the y intercept is 2

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