In the xy coordinate plane, does the point (3,4) lie on line

Keep in mind, there are two ways in which you can define a line t:
- You are given two distinct points that lie on that line. You join the two points and you have a defined line.
- You are given one point and the slope of the line. You make a line with the given slope on the point.

Question: In the xy coordinate plane, does the point (3,4) lie on line t?
You need to define line t to figure out if a point lies on it.

(1) The line 5y-45=-x is perpendicular to the line t.

This gives you the slope of line t but you don't have any point on it. So you cannot define line t.
Not sufficient.

(2) The line with the equation \(y= \frac{3}{4}x - 11\) intersects the line t when y=-11.
When y = -11, you can find the value of co-ordinate x by plugging in \(y= \frac{3}{4}x - 11\).
So you will have a point which lies on line t. But you don't have another point.
Hence you cannot define line t using this statement alone.

Using both stmnts, you get the slope of line t and a point that lies on it. This will help you define t uniquely. So you will be able to find out whether (3, 4) lies on it.
Sufficient.

Answer (C)

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