Is it true that a linear equation determines a line in the x-y plane

True

Step-by-step explanation:

A linear equatin in the xy plane contains two variables x and y and the power of both x and y should always be 1

The std form of a linear equation is

ax+by+c =0

Let us prove that this repesents a straight line only.

Consider the equation ax+by+c=0

Differentiate wrt x

a + b y' =0

Or y' = -b/a

In other words the slope of the curve is not dependent on the points taken but constant.

This ensures constant variation of y over x.

Hence this is nothing but a straight line in xy plane.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

there is no grid

step-by-step explanation: