Suppose the graph of a line has a negative slope and a positive y-intercept. Through which quadrants does the line pass? Justify your reasoning.

Question

We are learning about the slope and y-intercept

Answer 1

y = Mx + b  where M<0 and b>0

 

For x<0, Mx > 0 , which means Mx+b > 0.

So when x<0 y > 0 which lies in quadrant 2.

 

For x=0, y=b > 0 which is the positive y axis in between quadrants 1 and 2.

 

for x > 0, Mx < 0.

  So Mx + b can be either positive or negative depending on x.

 

    That means the line is in either quadrants 1 or 4.

 

 

SUPPOSE the line is in quadrant 3, where x and y are both negative.

Then x<0 and y < 0.

 

Mx > 0 <--- negative times negative is positive.

since b>0, y = Mx +b > 0.

which contradicts the assumption that y<0.

So the line CANNOT be in quadrant 3.

 

Therefore the line passes through quadrants 1,2,and 4