Which line has the following intercepts?
x-intercept = (3/7, 0); y-intercept = (0, -1/2)
A. 7x + 6y = 3
B. 7x - 6y = 3
C. 7x + 6y = -3
D. 7x - 6y = -3
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To determine which line has the given intercepts, we need to substitute the x-intercept and y-intercept values into the equation of each line and see if they satisfy the equation. If they do, then that line is the correct one.
Let's start with option A: 7x + 6y = 3
Substituting the x-intercept (3/7, 0) into the equation:
7(3/7) + 6(0) = 3/1 + 0/1 = 3/1 = 3
Since the result is not equal to 0, this line does not pass through the x-intercept (3/7, 0), so it is not the correct line.
Let's move on to option B: 7x - 6y = 3
Substituting the x-intercept (3/7, 0) into the equation:
7(3/7) - 6(0) = 3/1 - 0/1 = 3/1 = 3
Since the result is again not equal to 0, this line does not pass through the x-intercept (3/7, 0). So, option B is not the correct line.
Next, let's try option C: 7x + 6y = -3
Substituting the x-intercept (3/7, 0) into the equation:
7(3/7) + 6(0) = 3/1 + 0/1 = 3/1 = 3
Once again, the result is not equal to 0, meaning this line does not pass through the x-intercept (3/7, 0). Therefore, option C is also not the correct line.
Finally, let's check option D: 7x - 6y = -3
Substituting the x-intercept (3/7, 0) into the equation:
7(3/7) - 6(0) = 3/1 - 0/1 = 3/1 = 3
As before, the result is not equal to 0, so this line does not pass through the x-intercept (3/7, 0). Thus, option D is not the correct line.
None of the options satisfy the x-intercept condition. Therefore, it seems there is no correct option provided.