K is a line on x-y plane, what is the slope of k? 1)

Question

K is a line on x-y plane, what is the slope of k?

1) x-intercept of k is 2
2) y-intercept of k is 3

freetheking · Answer

let k = ax+b, slope of k is a.

stmt1. 
(2,0) is on k.
thus 0 = 2a+b => insuff.

stmt2.
(0,3) is on k
thus, 3 = b => insuff.

stmt1+2
0 = 2a + b
b=3
solve for a
a = -3/2 suff.

thus, C.

jaynayak · Answer

let the line be y = mx +b

1) x intercept is 2
hence point is (2,0)
0 = 2m + b
Not suff

2) y intercept is 3
point (0,3)
3 = m*0 + b
hence b = 3 
Not suff

Together

0 = 2m + 3
m = -3/2

gmatmathguru · Answer

Note that through any given point in xy plane, you can draw infinite lines. So, obviously statement 1 and 2 are insufficient.

However, given x and y intercept, note the following that will come in handy in solving problems:

given an x intercept say a, and y intercept, say b, note the following properties:

1. The line goes through the point (a,0) and (0,b) because on x-axis y co-ordinate is zero and on y-axis x coordinate is zero.

2. The slope can be easily found out by the formula (y2-y1)/(x2-x1) = -b/a

3. The equation of the line given the x intercept and y intercept is x/a + y/b = 1.

look at the simplicity of this equation, it will satisfy the property 1, if you plug in x=0 or y =0.

4. given x and y intercept as a and b, the line forms a right triangle with the origin (0,0), (a,0) and (0,b). This triangle has the area of |1/2 * a * b|
because the base is a and the height is b.

Coming back to the problem, the answer is C.

-mathguru

K is a line on x-y plane, what is the slope of k? 1)

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