Slopes.Calculate the slope of the line that has the equation 4x+2y=12 .

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

To find the slope, we need two points from the line.

If x = 0, 2y = 12 and y = 6.  This means that one of our points is (0,6)

If y = 0, 4x = 12 and x = 3.  This means that another point is (3,0).

To find the slope, we use the formula

m = (y1 - y2)/(x1 - x2)

m = (6 - 0)/(0 - 3)

m = 6/-3

m = -2

The slope of this line is -2.

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

4x + 2y = 12

This is in the standard form. Lets change it to slope-intercept form by solving for y. 

2x + y = 6  (divide out the 2s)

y = -2x + 6

This is in the slope-intercept form: y = mx + b where m is the slope. Knowing this, its easy to see that -2 is the slope. 

Jyotsana's profile pic

Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

Posted on

4x+2y=12

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

2y=12-4x

2y/2=12/2-4x/2

y=6-2x

y=-2x+6

slope=-2

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll write 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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