First problem: The equation for the line is y = mx + 4, and we know that m is negative.
The x intercept occurs when y = 0. plug that into the line and solve for x:
0 = mx + 4
x = -4/m
Note that m cannot be zero since m is negative. Also, note the sign of x -- since m is negative, a negative divided by a negative is positive. So the answer has to be a positive number. The only possible option is 6.
That's the algebraic approach. It's best to draw the line. Plot the y-intercept, (0,4). The slope is negative so we know that direction of the line is the top left to the bottom right.
Can it possibly intersect the x axis at a negative number? It should be easy to convince yourself the answer is no.
Can it run through the origin? Only if the line was vertical, but that would mean the slope is undefined. And we know the slope is negative. We can have a very negative slope and get as close to zero as possible, but we can never actually get there with a negative slope.
Looking at our quick sketch again, we see that 6 is possible.
