sana.noor wrote:In the coordinate plane, line A is defined by the equation 3x + 2y = k, and line B is defined by the equation jx-y=-7. At what point do the two lines intersect?
(1) Line A passes through the point (0,7)
(2) Line B passes through the point (3,1)
Target question:
At what point do the two lines intersect?
Given: line A is defined by the equation 3x + 2y = k, and line B is defined by the equation jx - y = -7
One strategy is to rewrite both equations in slope y-intercept form to get a better idea of how the variables k and j affect the lines.
We get line A: y = -3/2 x + k/2 (here we see that the slope of line A is -3/2, and k affects the line's y-intercept)
We also get line B: y = jx + 7 (here we see that j affects the slope of the line, and the
y-intercept is 7 )
Statement 1: Line A passes through the point (0,7)
This tells us that the
y-intercept of line A is 7.
Hey, the y-intercept of line B is also 7!
So,
the two lines must intersect at (0,7)
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: Line B passes through the point (3,1)
Remember that line B is defined by the equation y = jx + 7
So, if we plug x = 3 and y = 1 into the equation we can determine the value of j.
In fact, we get j = -2
So, line B is defined by the equation y = -2x + 7
However, this information tells us nothing about line A. All we know about line A is that it has slope of -3/2.
Since we don't know the y-intercept of line A, we have no idea where line A is located on the coordinate plane.
If we can't fix line A's position in the coordinate plane,
we cannot determine its intersection with line B
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer =
A
Cheers,
Brent
