Question

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.

Answer 1

Answer is b

Explanation:

Answer 2

Option B is correct

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

Explanation:

Slope-intercept form:

The equation of line is given by:

`y=mx+b`

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:

`\text{Slope}= (y_2-y_1)/(x_2-x_1)`

Substitute the given points we have;

`\text{Slope}= (10-6)/(3-1)`

⇒
`\text{Slope}= (4)/(2)`

Simplify:

⇒
`\text{Slope}=2`

⇒
`\text{Slope}= (4)/(2)`

⇒ 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.