To find the slope of the line from the equation 3x + 2y = 8, we first need to rearrange it into the slope-intercept form, which is given by:
y = mx + b
where m represents the slope and b represents the y-intercept.
Starting with the original equation:
3x + 2y = 8
We want to isolate y. First, subtract 3x from both sides:
2y = -3x + 8
Next, divide every term by 2 to solve for y:
y = -\frac{3}{2}x + 4
Now, it’s clear that the equation is in the slope-intercept form y = mx + b, where:
- m (the slope) is -3/2
- b (the y-intercept) is 4
Thus, the slope of the line represented by the equation 3x + 2y = 8 is -\frac{3}{2}.
This means for every 2 units you move to the right along the x-axis, the line will move 3 units down along the y-axis.