Problem Solving

Hi All,

We're told that in the coordinate plane, Line A has a slope of -1 and an x-intercept of 1 and Line B has a slope of 2 and a y-intercept of -2. The two lines intersect at the point (a,b). We're asked for the sum a and b. When dealing with lines, it often helps to write the given information in 'Slope-Intercept' format (re: Y = (M)(X) + B).

Line A has a slope of -1 and an x-intercept of 1....
Y = (-1)(X) + B
0 = (-1)(1) + B
0 = -1 + B
1 = B

Thus, Line A is Y = (-1)(X) + 1

Line B has a slope of 2 and a y-intercept of -2
Y = (2)(X) + B
-2 = (2)(0) + B
-2 = 0 + B
-2 = B

Thus, Line B is Y = (2)(X) - 2

To find the intercept point, you can either graph the two lines or set the two equations equal to one another (since we know that the 2 lines will intercept at one point)...

Y = (-1)(X) + 1
Y = (2)(X) - 2
(-1)(X) + 1 = (2)(X) - 2
3 = 3X
1 = X

When X=1, Y=0, so the intercept point is (1,0) and the sum of a and b is 1+0 = 1.

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:Veritas Prep

In the coordinate plane, Line A has a slope of -1 and an x-intercept of 1. Line B has a slope of 2 and a y-intercept of -2. If the two lines intersect at the point (a,b), what is the sum a+b?

A. 0
B. 1
C. 2
D. 3
E. 4

OA B

We see that an equation of line B is y = 2x - 2. Let's let the equation of line A be y = -x + k, where k is the y-intercept. Since line A contains the point (1, 0), we have:

0 = -1 + k

1 = k

Therefore, an equation of line A is y = -x + 1. Since the two lines intersect, we can find their point of intersection (a, b) by setting their equations equal to each other:

2x - 2 = -x + 1

3x = 3

x = 1

In other words, a = 1. So y = 2x - 2 = 2(1) - 2 = 0 or b = 0. Therefore, a + b = 1 + 0 = 1.

Answer: B