Which of the following functions
increases at a higher rate?
The graph with the steeper slope or
gradient will be the function that increases at the higher rate. At first glance, it appears that
graph B has a steeper slope or gradient than graph A. However, in order to get a more
accurate answer, we need to calculate the slope of both of the lines.
We do this using the formula 𝑦 two
minus 𝑦 one divided by 𝑥 two minus 𝑥 one, where 𝑥 one, 𝑦 one and 𝑥 two, 𝑦 two
are two points on the line. The two coordinates or ordered
pairs marked on graph A are negative one, zero and zero, one.
Substituting these values into the
formula gives us one minus zero divided by zero minus negative one. One minus zero is equal to one. And zero minus negative one is the
same as zero plus one, which also equals one.
Therefore, the slope of function A
is equal to one. The two coordinates that are marked
on graph B are negative one, zero and zero, six. We can calculate the slope of graph
B in a similar way, six minus zero divided by zero minus negative one. This gives us six divided by one,
which is equal to six.
As the gradient or slope of B is
greater than the slope of A, we can say that function B increases at a higher
rate. This method can be used to compare
the rate of change of any linear functions.