A student chose (4, 0) and (0, 3) to graph 3x + 4y = 12. How is this choice?
Answer and explanation
Correct answer: Correct
The governing graphical principle is that two distinct points satisfying a linear equation determine its straight-line graph. Test (4, 0): 3(4) + 4(0) = 12 + 0 = 12, so it lies on the line. Test (0, 3): 3(0) + 4(3) = 0 + 12 = 12, so it also lies on the line. These are the x-intercept and y-intercept respectively, and they are distinct points, so joining them gives the required graph. Therefore option A is correct. Option B is false because (4, 0) satisfies the equation, and option C is false for the same reason regarding (0, 3). Option D is false because the coordinates are different, not identical.
Frequently asked questions
What is the correct answer to this question?
Correct
Why is this the correct answer?
The governing graphical principle is that two distinct points satisfying a linear equation determine its straight-line graph. Test (4, 0): 3(4) + 4(0) = 12 + 0 = 12, so it lies on the line. Test (0, 3): 3(0) + 4(3) = 0 + 12 = 12, so it also lies on the line. These are the x-intercept and y-intercept respectively, and they are distinct points, so joining them gives the required graph. Therefore option A is correct. Option B is false because (4, 0) satisfies the equation, and option C is false for the same reason regarding (0, 3). Option D is false because the coordinates are different, not identical.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
