sana.noor wrote:(77) In an xy-coordinate plane, a line is defined by y = kx + 1. If (4, b), (a, 4), and (a, b +1) are three points on the line, where a and b are unknown, then k = ?
a) 1/2
b) 1
c) 1 and 1/2
d) 2
e) 2 and 1/2
There's a HUGE CLUE in the fact that (a, 4) and (a, b+1) are both on the same line. Notice that the x-coordinates are the same. If the x-coordinates are the same, then there are two possible scenarios:
scenario #1: The points (a, 4) and (a, b+1) are DIFFERENT points, in which case the line is vertical (with undefined slope)
scenario #2: The points (a, 4) and (a, b+1) define the SAME point
IMPORTANT: If a line is defined by y = kx + 1, then k represents the slope. So, the question is really asking us to find the slope of the line.
In scenario #1, the slope would be undefined. Since none of the answer choices are undefined, we can rule out scenario #1, which means (
a,
4) and (
a,
b+1) define the SAME point. So, we can be certain that
b+1 =
4, which means
b = 3
Now that we know that
b = 3, we can use the fact that the point (4,
b) is on the line.
This means that the point (4,
3) is on the line y = kx + 1.
When we plug x=4 and y=3 into the equation, we get 3 = (k)(4) + 1
Solve to get k = 1/2
Answer:
A
Cheers,
Brent
