Function 1: y = 4x + 5
function 2: the line passing through the points (1, 6) and (3, 10).

which of these functions has the greater rate of change?
a) function 1, because the slope is 5 and the slope of function 2 is 4.
b) function 1, because the slope is 4 and the slope of function 2 is 2.
c) function 2, because the slope is 7 and the slope of function 1 is 5.
d) function 2, because the slope is 5 and the slope of function 1 is 4.

Option B is correct

Function 1, because the slope is 4 and the slope of function 2 is 2.

Step-by-step explanation:

Slope-intercept form:

The equation of line is given by:

where, m is the slope and b is the y-intercept

As per the statement:

Function 1: y = 4x + 5

On comparing with [1] we have;

Slope of function 1  = 4

Function 2: The line passing through the points (1, 6) and (3, 10).

Using slope formula:

Substitute the given points we have;

⇒

Simplify:

⇒

⇒

⇒ Slope of the function 2 is, 2

Since, function 1 is greater rate of change.( i.e 4 > 2)

Therefore,

Function 1  has the greater rate of change,  because the slope is 4 and the slope of function 2 is 2.

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