What is the slope, m, and the coordinates of the y-intercept for the graph represented by this equation: 3x+2y=12 ?
m =
y-intercept = ( , )
To find the slope-intercept form of this linear equation, we need to isolate the y variable.
Starting with the given equation:
3x + 2y = 12
Subtracting 3x from both sides:
2y = -3x + 12
Dividing by 2:
y = (-3/2)x + 6
The slope, m, in the slope-intercept form (y = mx + b) is the coefficient of x. In this case, m = -3/2.
The y-intercept is the point where the graph intersects the y-axis. It can be found by substituting x = 0 into the equation and solving for y:
y = (-3/2)(0) + 6
y = 6
Therefore, the y-intercept is (0, 6).