Is point (3, 4) on line K? 1) Line K crosses the Y-axis at (0.5) 2) Th

Hi,

If you can draw a line on the graph, we can find which all points are on the line.
Here, Statement I gives you coordinates of one point and statement II gives you the slope, so you can draw the line that is unique.
Now you can find whether the point is there on line. HOW? not required as we have a yes to can we find. Sufficient and C.
See the attached figure.

Proper method..
1) Line K crosses the Y-axis at (0.5)
So coordinates of one point is (0, 0.5), but it can lead to infinite lines passing through this point.
Insuff

2) The slope of line K is 2
We can draw infinite lines that have slope 2, but each will be parallel to each other.
Also \(\frac{y-y_1}{x-x_1}=2\) we have 4 variables..Insuff

Combined..
Since line passes through (0,0.5), \(\frac{y-y_1}{x-x_1}=2\) becomes \(\frac{y-0.5}{x-0}=2....y-0.5=2x\)
Equation of the line => y=2x+0.5
To check whether (3,4) is on the line, substitute x=3, and see whether y is 4..
\(y=2*3+0.5=6.5\neq{4}\)
So point is NOT on the line..
Suff

C

Asked: Is point (3, 4) on line K?
y = mx + c; where m is slope of the line and c is the y-intercept of the line.
To check whether a point (3,4) lies on the line K, line K should be well defined.

1) Line K crosses the Y-axis at (0.5)
c = 0.5
Since slope of line K is unknown
NOT SUFFICIENT

2) The slope of line K is 2
m=2
since y-intercept is unknown
NOT SUFFICIENT

(1) + (2)
1) Line K crosses the Y-axis at (0.5)
2) The slope of line K is 2
y = 2x + 0.5
If x=3; y = 6.5
The point (3,4) does not lie on line K.
SUFFICIENT

IMO C

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