4x + 3y = 12
We must get it in the slope-y-intercept form: y = mx + b.
We subtract 4x from both side:
4x + 3y = 12
-4x -4x
-------------------
3y = 12 - 4x
We swap the terms on the right because the form y = mx + b has the x term first
3y = -4x + 12
We divide all three numbers by 3
y = x +
Simplify
y = x + 4
Next we compare that to
y = mx + b which has slope m and y-intercept (0,b)
We can see that m = and that b = 4 so the y-intercept
is the point (0,4)
The graph is below. Notice that the y-intercept is the point (4,0)
That's where the line crosses the y-axis. Notice that it goes
downhill as you move to the right. That tells us that the slope is
a negative number. Notice that it rises up to 4 (the numerator of the
slope) on the y-axis, and that it runs out to 3 (the denominator of the
slope) on the x-axis.
Edwin
