SOLUTION: if a line cuts the positive x-axis and the positive y-axis it has a negative gradient true or false or sometimes true i have no idea this is the last one on my homework shee

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Question 1039567: if a line cuts the positive x-axis and the positive y-axis it has a negative gradient
true or false or sometimes true
i have no idea this is the last one on my homework sheet, all help is appreciated!
Found 2 solutions by jim_thompson5910, Fombitz:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
"if a line cuts the positive x-axis" means the x intercept must have a positive x coordinate, eg: (5,0)

"if a line cuts...the positive y-axis" then we know the y intercept has a positive y coordinate, eg: (0,8)

Let's find the slope of the line through those two example points

m = (y2 - y1)/(x2 - x1)

m = (8 - 0)/(0 - 5)

m = 8/(-5)

m = -1.6

Which is a negative slope or gradient (slope and gradient mean the same thing).

It turns out that the slope will always be negative in this case. As long as the x intercept is on the positive x axis and the y intercept is on the positive y axis, then the slope will always be negative.

So the final answer is True.

Side Note: I recommend you trying out other possible x and y intercepts. Compute the slope and hopefully you'll find that the slopes will always be negative.

Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
It cuts the x axis at (,) where .
It cuts the y axis at (,) where .
Since you have two points, you can calculate the slope(gradient) of your line,

Since both and are positive, is positive and then
True.