In the rectangular quadrant system shown...

AAPL wrote:

In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation 3x + 5y = -2?

A. none
B. I
C. II
D. III
E. IV

One option is to use some number sense.
Notice that for two values (x and y), to satisfy the equation 3x + 5y = -2, at least one of the values (x or y) must be NEGATIVE.
Conversely, we should recognize that x and y cannot both be POSITIVE
Otherwise we have the equation 3(POSITIVE) + 5(POSITIVE) = -2, which is impossible.

If x and y cannot both be POSITIVE, (x,y) cannot be in quadrant I, since all points in quadrant I are such that the x and y coordinates are both POSITIVE

Answer: B

Cheers,
Brent

AAPL wrote: I need to re-write the equation of the following form,

$$y=-\frac{3}{5}x-\frac{2}{5}$$

Now I can draw the line and get the solution for this PS question, right?

Yes, that's a great approach.
Now you know that the y-intercept is -2/5 AND the slope is negative.
When you sketch the graph, you'll see that the line does NOT pass through quadrant I

Cheers,
Brent