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.

2 Answers
Jun 23, 2018

#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#

Jun 23, 2018

#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