Question

function 1 is defined by the equation $p = r + 7$. function 2 is defined by the following table.

$r$	$p$
1	9.1
5	13.5
10	19

which function has a greater slope? choose 1 answer: a function 1 b function 2 c the functions have the same slope.

Explanation:

Step1: Find slope of Function 1

Function 1 is \( p = r + 7 \), which is in slope - intercept form \( y=mx + b \) (here \( y = p \), \( x = r \), \( m \) is slope, \( b \) is y - intercept). So the slope of Function 1, \( m_1=1 \).

Step2: Find slope of Function 2

The slope formula is \( m=\frac{p_2 - p_1}{r_2 - r_1} \). Let's take two points from the table of Function 2. Let's take \( (r_1,p_1)=(0,8) \) and \( (r_2,p_2)=(1,9.1) \).
Using the slope formula, \( m_2=\frac{9.1 - 8}{1 - 0}=\frac{1.1}{1}=1.1 \). We can check with other points. For example, take \( (r_1,p_1)=(0,8) \) and \( (r_2,p_2)=(5,13.5) \). Then \( m_2=\frac{13.5 - 8}{5 - 0}=\frac{5.5}{5}=1.1 \). And for \( (r_1,p_1)=(0,8) \) and \( (r_2,p_2)=(10,19) \), \( m_2=\frac{19 - 8}{10 - 0}=\frac{11}{10}=1.1 \). So the slope of Function 2, \( m_2 = 1.1 \).

Step3: Compare the slopes

Since \( 1.1>1 \), i.e., \( m_2>m_1 \), Function 2 has a greater slope.

Answer:

B. Function 2