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

You can find the slope of both lines and then the equation of both lines and solve the system of the two equations,. But since the answer choices are just the quadrants, an answer can be found quicker by just sketching the two lines.


You can see that the intersection will be in Quadrant IV, where x >0 and y <0, so the answer is B.

Take care.

alanforde800Maximus wrote:In the xy-plane, line l passes through the points (0,2) and (1,0), and line m passes through the points (0,-4) and (4,0). If (a,b) is the point of intersection of line l and line m, which of the following is true?

a) a > 0 and b > 0
b) a > 0 and b < 0
c) a < 0 and b > 0
d) a < 0 and b < 0
e) a = 0 or b = 0

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