What is the slope of the line that has the equation 4x + 2y = 12?

Question

my class was given this as a study for a final please help me understand how to do this as well as show me from what your stared with to your conclusion

Answer 1

The Standard Form of the equation of a line is:  Ax+By=C

The slope-intercept form of the equation of a line is:  y=mx+b

      where m=slope, point (0,b) is y-intercept

 

Now, once and forever (and remember it!), convert Ax+By=C to

  the form y=mx+b and get:  y = (-A/B)x + C/B

 

That means that the slope of the given line (4x + 2y = 12) is (-4/2)=-2.

Answer 2

Hi Dakota

 

The equation you have been given is what is called the standard form of an equation of a line.

 

There are two other forms, the point-slope form: y-y₁ = m(x-x₁)

and the slope intercept form: y=mx+b

 

The slope intercept form is probably the one most of us are familiar with and what we think of when we think of an equation of a line.  What's great about the slope intercept form is you can find the slope of the line without and further calculation once you have the line equation in that form.

 

So let's start with the equation you were given and see what we can do with it.

 

4x+2y=12

 

Let's rearrange terms to isolate the y, in other words, solve for y in terms of x.

 

4x+2y=12

-4x       -4x

----     -----

0 + 2y = -4x+12

or

2y = -4x+12

 

Now divide by 2

2y = -4x+12

---   ---    ---

2      2     2

 

y = -2x+6

 

This is in the slope intercept form and we have m (slope) = -2

 

Answer 3

4x+2y=12

put the equation in the slope-intercept form

y=mx+b where m is the slope and b is the y-intercept

 

4x+2y=12

2y=-4x+12

y=-4x/2+12/2

y=-2x+6

y=mx+b

m=-2 which is the slope