To determine which of the given options (A, B, C, D) is the largest, let's evaluate each one:
A: The x-intercept of 3x - 4y = 12 can be found by setting y = 0 and solving for x:
3x - 4(0) = 12
3x = 12
x = 12 / 3
x = 4
B: The slope between the points (3, 2) and (0, 1) can be found using the formula for slope (m):
m = (y2 - y1) / (x2 - x1)
m = (1 - 2) / (0 - 3)
m = (-1) / (-3)
m = 1/3
C: The slope of the line 2x - 3y = 0 can be determined by rearranging the equation into slope-intercept form (y = mx + b):
2x - 3y = 0
-3y = -2x
y = (2/3)x
So, the slope is 2/3.
D: The y-intercept of 3x + 4y = 12 can be found by setting x = 0 and solving for y:
3(0) + 4y = 12
4y = 12
y = 12 / 4
y = 3
Now, let's compare these values:
A: x-intercept = 4
B: slope between (3,2) and (0,1) = 1/3
C: slope of the line 2x-3y=0 = 2/3
D: y-intercept = 3
The largest value among these options is the x-intercept in option A, which is 4.