Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x)= 4x + 2 The function g(x) going through 0, −2 and 1, 3 The function f(x) has a larger slope. The function g(x) has a larger slope. They both have the

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

`f(x)= 4x + 2` The function `g(x)` going through `(x,y)=(0, −2) and (x,y)=(1, 3)`

The function `f(x)` has a larger slope.
The function `g(x)` has a larger slope.
They both have the same slope.
The relationship between slopes cannot be determined.

Answer 1

`f(x)=4x+2`, `g(x)=5x-2`
Therefore `g(x)` has a larger slope.

Explanation:

The slope is the constant in front of x, i.e. f(x) has a slope of 4

The way I understand your statement, you mean that g(x) goes through the points (0, -2) and (1, 3) (otherwise one might understand your statement that g(x) is, 0, -2, 1, 3 for some values of x).
(Please remember to write precisely what you are asking, otherwise you risk misunderstanding of your question.)

From this it follows that `g(0)=-2` and `g(1)=3`,
i.e. `g(x)` increases (has a slope of) `3+2=5` when x increases fro 0 to 1.

Therefore g(x) has a greater slope than f(x).

If we write g(x)=ax+b
we have `a*0+b=-2` => `b=-2`
`a*1-2=3` => `a=5`
Therefore, `g(x)=5x-2`

Answer 2

`g(x)` has the 'greater' slope

Explanation:

The slope of `f(x)` is such that it 'goes up' 4 for 1 along.

Lets have a look at `g(x)`

The slope (gradient) is determined by reading along the x-axis from left to right. Thus using `x` the left most point `P_1->(x_1,y_1)=(0,-2)` and the right most point `P_2->(x_2,y_2)=(1,3)`

For the slope we have

`P_2-P_1 = ("change in y")/("change in x") =(y_2-y_1)/(x_2-x_1) = (3-(-2))/(1-0)=5/1=5`

So for the gradient:

`g(x)->5`
`f(x)->4`

Thus `g(x)` has the 'greater' slope

Bad practice to use the word 'larger' for a measure of slope