In the xy-plane, line l passes through the points (0,2) and (1,0), and

We can begin by finding an equation for each line:

Line l:

slope = (0-2)/(1-0) = -2, y-intercept = (0, 2) = 2

Thus, an equation for line l is y = -2x + 2

Line m:

Slope = (0-(-4)/(4-0) = 1, y-intercept = (0, -4) = -4

Thus, an equation for line m is y = x - 4.

Now, let’s find their intersection by setting the right hand side of the two equations equal to each other:

-2x + 2 = x - 4

-3x = -6

x = 2

Substitute x = 2 back to either equation (let’s take the one for line m), we have:

y = 2 - 4 = -2

We see that the point of intersection is (2, -2), so a = 2 > 0 and b = -2 < 0.

Alternate Solution:

Using the given points, make a quick sketch of the two lines on the same set of coordinate axes. Note that line l has a negative slope and line m has a positive slope. Their point of intersection will be in Quadrant 4, where x is always positive and y is always negative.

Answer: B