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 sl…

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asked Aug 15, 2017 46.2k views

2 Answers

Esylvestre · Answer 1 · 2017-08-21T12:30:43+0000

Answer:

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.