Comparing linear functions: equation vs. graph

two functions F and G are described below which of these statements about F and G is true so they defined function f as kind of a traditional linear equation right over here and this right over here is G so this right over here is G of X and that also looks like a linear function we see it's a kind of a downward sloping line so let's look at our choices and see which of these are true f and G are both increasing and F is increasing faster than G well when I look at G well first of all G is definitely decreasing so we already know that that's false and F is also decreasing we see here it has a negative slope every time we move forward three in the X direction we're going to move down seven in the vertical direction so neither of these are increasing so that's definitely not right F and G are both increasing well that's definitely not right so we know that both F and G are decreasing so this first choice is they're both decreasing and G is decreasing faster than F so let's see what the slope on G is so the slope on G is every time we move one in the X Direction positive one in the X direction we move down we move down two in the Y direction so for G of X if we were to write our change in Y over our change in X which is our slope our change in Y of our change in X when we move one in the X Direction positive one in the X direction we move down two in the Y direction so our change in Y over change in X is negative two so G has a slope of negative two F has a slope of negative 7/3 negative 7/3 negative 7/3 is the same thing as negative two and one third so f slope is more negative so it is decreasing faster so G is not decreasing faster than F f is decreasing faster than G so this is not right and then we have this choice F and G are both decreasing and F is decreasing faster than G this is right right over here we have this last choice G is increasing but F is decreasing we know that's not true G is actually decreasing