Question

Graph the ordered pairs (-2, -1) and (3, -5) and draw a line through the two points. Which quadrant is untouched by the line? Explain how you found your answer.

Answer 1

find the slope between both points
\[slope = m = \frac{y2-y1}{x2-x1}\]
then use the point slope form to find the line
\[(y-y1) = m(x-x1)\]

Answer 2

Honestly they are tellling you to draw this line and then they are asking how you found your answer ? XD It is right there, i just read it from the picture.
But illogicality aside, you can see that those points lay in quadrants 3 and 4. Thus the only possible quadrants that this line does not touch are, 1 and 2. So now we can see that as value of x rises the value of y declines. So for an arbitrarrly low x, y is arbitrarrly high. So there is a point which has a negative value of X and positive value of Y. So this line also touching second quadrant. So the only quadrant not thouched by thus line is by process of elimination discovered to be the first one .