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

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the equation of the line as : 4x+2y=12

Now 4x+2y=12

=> 2y = 12 - 4x

=> y = 6 - 2x

A line with a slope m and y-intercept c can be written as y = mx + c

In the case of y = -2x - 6, the slope is -2.

The required slope is -2.

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

The slope of the line ax+by+c = 0 is gotten by writing the equation in the slope intercept form y = mx+c, where m is the slope and c is the y intercept.

ax+by+c = 0.

=> by = -ax-c.

y = (-a/b) +(-c/a), where (-a/b) is the slope of the line ax+by+c = 0.

So 4x+2y = 12 could be written as:

2y = -4z+12.

=>  2y/2 = (-4x/2)+12/2.

=> y = -2x+6 which is in slope intercept form like y = mx+c. So slope m = -2.

So the slope of the line 4x+2y= 12 is -2.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First, we need to put the equation in the point slope form:

Y = mx + n, where m represents the slope.

For this reason, we'll have to subtract 4x both sides:

4x - 4x + 2y = 12 - 4x

We'll eliminate like terms:

2y = -4x + 12

We'll divide by 2:

y = -4x/2 + 12/2

We'll simplify and we'll get:

y = -2x + 6

The slope is m = -2.

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