Answer:
The statement which correctly compares the slopes of two functions is:
- Function f(x) has a slope 2, which makes is steeper than g(x)
Step-by-step explanation:
If the slope of a function has a greater absolute value as compared to other then that function is steeper than the other.
Here we have a function f(x) as:
[tex]3x-y=6[/tex]
On changing to slope-intercept form of a line
i.e. y=mx+c
where m is the slope of the line and c is the y-intercept of the line we have:
[tex]f(x)=y=3x-6[/tex]
i.e. the slope of function f(x) is: 3
The function g(x) is a graph that passes through (-2,1) and (-1,3)
The equation for y=g(x) is given by:
[tex]y-1=\dfrac{3-1}{-1-(-2)}\times (x-(-2))\\\\\\y-1=\dfrac{2}{-1+2}\times (x+2)\\\\\\i.e.\\\\\\y-1=\dfrac{2}{1}\times (x+2)\\\\\\i.e.\\\\\\y=2x+4+1\\\\\\i.e.\\\\\\y=2x+5[/tex]
( since we used a concept of a line passing through two-point (a,b) and (c,d) is given by the equation:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex] )
Hence, the slope of function g(x) is: 2
The absolute value of slope of function f(x) is greater than function g(x)
( since 3>2 )
Hence, we get function f(x) is more steeper.
