explain why the graph of x + y = k cannot pass through the quadrant III if k > 0.
Your School Subject is NOT college.
To understand why the graph of the equation x + y = k cannot pass through quadrant III when k > 0, we need to analyze the properties and characteristics of quadrant III.
Quadrant III is the section of a coordinate plane where the x-coordinate is negative (less than zero), and the y-coordinate is also negative. In other words, both x and y values in this quadrant are less than zero.
Now, let's consider the equation x + y = k.
If we substitute x = 0 and y = 0 into the equation, we get:
0 + 0 = k
0 = k
This means that the point (0, 0) always satisfies the equation for any value of k, including when k > 0.
However, in quadrant III, both x and y values are negative. If k is a positive value, it implies that one of the variables (either x or y) has to be positive to compensate for the positive k value. This is not possible in quadrant III, as both x and y values are negative.
Therefore, the graph of x + y = k cannot pass through quadrant III when k > 0, because the equation implies the existence of a positive value, contradicting the nature of quadrant III where both x and y values are negative.