Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x)= −1x + 1

aThe function f(x) has a larger slope.
 bThe function g(x) has a larger slope.
 cThey both have the same slope.
 dThe relationship between slopes cannot be determined.

Answer 1

They have the same slope. The slope of f(x) is 3 because it is the m in f(x)=mx+b. In the graph of g(x), the slope can be found by change in y divided by change in x, or rise over run. Between x=0 and x=1, the y value increases by three, from 2 to 5. The slope of g(x) is 3/1=1.

Hope this helps!

Answer 2

Answer with explanation

The Function , f(x)= -1 x +1

Slope of f(x)=-1

Equation of function , g(x),that is, line passing through ,(0,3) and (2,-1) can be obtained by

Equation of line passing through two points ,
`(x_(1),y_(1)), (x_(2),y_(2))` is,

`(y-y_(1))/(x-x_(1))=(y_(2)-y_(1))/(x_(2)-x_(1))`

→
`(y-3)/(x-0)=(3+1)/(0-2)\\\\ (y-3)/(x)=(4)/(-2)\\\\y-3=-2 x\\\\ 2 x+y=3`

g(x)= 2 x+y=3

y= -2 x+3

Slope of g(x)= -2

-1 > -2

So, Slope of f(x) > Slope of g(x)

Option a: The function f(x) has a larger slope.